the demand for video streaming services such as those offered by netflix , youtube , amazon , and others , is growing rapidly .this places a significant burden on networks .one way to mitigate this burden is to place memories into the network that can be used to cache files that users may request . in this paper , we investigate how to optimally use these caches . in particular , we are interested in _ online _ algorithms for this problem , in which the operations of the cache have to be performed on the fly and without knowledge of future requests .the online caching problem ( also known as the paging problem in the context of virtual memory systems ) has a long history , dating back to the work by belady in 1966  .this problem has been investigated both for systems with a single cache  as well as for systems with multiple distributed caches .one solution to the caching problem that is popular in practice and for which strong optimality guarantees can be proved  is the _ least - recently used _( lru ) eviction policy . in lru , each cache is continuously updated to hold the most recently requested files , allowing it to exploit the temporal locality of content requests .the figure of merit adopted by the papers mentioned so far is the cache - miss rate ( or page - fault rate in the context of the paging problem ) , sometimes weighted by the file size .this cache - miss rate is used as a proxy for the network load . for systems with a _ single _cache , the weighted cache - miss rate and the network load are indeed proportional to each other , and hence minimizing the former also minimizes the latter .however , this proportionality no longer holds for systems with _ multiple _ caches . for such systems with multiple caches , a fundamentally different so - called _ coded cachingapproach is required .this coded caching approach has been recently introduced in  for the _ offline _ caching problem .  in this paper, we investigate _ online _ coded caching , focusing on a basic content distribution scenario consisting of a single origin server connected through a shared ( bottleneck ) link to a number of users each equipped with a cache of finite memory ( see fig . [fig : setting ] ) . the users issue a sequence of content requests from a set of popular files , and the goal is to operate the caches as well as the server such as to satisfy these requests with the minimum number of bits sent over the shared link .we consider the case where the set of popular files evolve according to a markov model and users select their demand uniformly from this set .files of size bits each is connected through a shared link to users each with a cache of size bits . in the figure , and . ]we approximately characterize the optimal long - term average rate of the shared link for this setting .we show further that the optimal online scheme performs approximately the same as the optimal offline scheme .this is perhaps surprising , since in the offline scheme caches are allowed to be updated in an offline fashion each time the set of popular files changes , whereas in the online scheme caches are updated in an online fashion based solely on the limited observations they have through the sequence of requests .  to evaluate the gain of coded caching in practical scenarios , we propose an online coded caching scheme termed _ coded least - recently sent _( lrs ) and simulate it on a demand time series derived from the dataset made available by netflix for the netflix prize . for this time series , we show that the proposed coded lrs algorithm significantly outperforms the baseline lru algorithm .the remainder of this paper is organized as follows .section [ sec : background ] provides background information on coded caching .section [ sec : problem ] formally introduces the problem setting .section [ sec : main ] contains the main results .the proof of these results are provided in section [ sec : proof1 ] .coded caching , recently introduced in , is a novel approach to the distributed caching problem .it can achieve a significant reduction in network load by creating and exploiting coded multicasting opportunities between users with different demands .we make essential use of the offline coded caching scheme from  in the present paper .therefore , we now briefly overview that algorithm and illustrate it with an example .the setting in  is the offline version of the one depicted in fig .[ fig : setting ] in section [ sec : intro ] . in particular , a single origin server is connected to users through a shared link .there is a fixed set of files of length bits , and each user has a memory of size bits with .the cache memories are prefetched in an _ offline _ fashion during a placement phase ( during a period of low network load , say the early morning ) so as to minimize the peak load over the shared link during a later delivery phase ( say in the evening ) during which each user requests a single file .we refer to the normalized peak load as the peak rate .the offline coded caching scheme proposed in  achieves a peak rate of which is shown to be within a constant factor of the optimal rate .  in the placement phase of the algorithm in  , each user caches a random subset of bits of each of the files . in the delivery phase , the server sends an appropriate linear combination of those bits over the shared link to enable all users to recover the requested files , as is illustrated in the following example .[ eg : dec ] consider the caching problem with files say and users , each with a cache of size . in the placement phase, each user caches bits of each file independently at random , satisfying the memory constraint .we partition where denotes the bits of file that are stored at the users in the set , and similarly for . for large enough, the size of the subfile tends to bits by the law of large numbers .  in the delivery phase , suppose that users one and two request files and , respectively .user one already has access to the file parts and of its requested file , and needs and , which are not cached its memory .similarly user two already has access to and of its requested file and needs and .the server can then satisfy these user requests by sending , , and over the shared link , where denotes the xor operation applied element - wise to to and treated as vectors of bits .observe that user one has stored in its cache . from this andthe output of the shared link , user one can recover the desired file part .similarly , user two has stored in its cache and can use this to recover the desired file part from the output of the shared link .thus , using the contents of their caches and the outputs of the shared link , both user can recover all the required subfiles .the rate over the shared link is where is defined in .while here the delivery phase is explained for a specific set of user requests , one can verify that this rate is achievable for all other possible requests as well .  the main gain from using this scheme derives from the coded multicasting opportunities between users with different demands .these coded multicasting opportunities are created in the placement phase and are exploited in the delivery phase . as the size of the cache memories increases , this coded multicasting gain increases as well .this gain , called the _gain in  , is captured by the factor in .there is a second , _ local _ , gain deriving from having part of the requested file available at a users local cache .this local gain is captured by the factor in . as is shown in  ,this local gain is usually less significant than the global coded multicasting gain .we consider a content distribution system with a server connected through a shared , error - free link to users as illustrated in fig .[ fig : setting ] in section [ sec : intro ] . at time , each user requests a file from a time - varying set of popular files with cardinality .the user s requests , collectively denoted by the vector , are chosen uniformly at random without replacement from .each file has size bits , and each user is equipped with a cache memory of size bits .the content distribution system operates as follows . at the beginning of each time slot ,the users reveal their requests to the server .the server , having access to the database of all the files in the system , responds by transmitting a message of size bits over the shared link . using their cache contents and the message received over the shared link , each user aims to reconstruct its requested file .  the goal is to design the actions of the users and the server such as to minimize the long - term average rate of the system , i.e. , while satisfying the memory and reconstruction constraints .observe that the rate is the long - term average load over the shared link normalized by the file size . in order to obtain a rate independent of the file size and to simplify the analysis, we allow the file size to be as large as needed .  in this paper , we are interested in _ online _ caching schemes , which place additional restrictions on the actions of the server and the caches . in such online schemes , the cache content at user at the beginning of timeslot is a function of the cache content at the same user at the previous time , the output of the shared link at time , and the requests up until time .in particular , the cache content may _ not _ be a function of the outputs of the shared link at times prior to .furthermore , for an online scheme , the message sent by the server over the shared link at time is a function of only the demands and the cache contents of the users at that time .we denote by the long - term average rate over the shared link of the optimal online caching scheme .[ eg : lru ] a popular online caching scheme is _ least - recently used _ ( lru ) . in this scheme ,each user caches entire files .when a user requests a file that is already contained in its cache , that request can be served out of the cache without any communication from the server .when a user requests a file that is not contained in the cache , the server sends the entire file over the link .the user then evicts the least - recently requested ( or used ) file from its cache and replaces it with the newly requested one .observe that this is a valid online caching strategy .indeed , the content of a user s cache at the beginning of time slot is a function of the cache content at time , the output of the shared link at time , and the past requests ( in order to determine which file was least - recently used ) .moreover , the message sent by the server at time is only a function of the demands and the cache contents of the users at that time ( in order to decide if a file needs to be transmitted at all ) .we will adopt lru as the baseline scheme throughout this paper .we next provide a formal description of the dynamics of the set of popular files .the initial set consists of distinct files .the set at time evolves from the set at time using an arrival / departure process . with probability , there is no new arrival and . with probability ,there is a new arrival , and the set is constructed by choosing a file uniformly at random from and replacing it with a new , so far unseen , file .note that this guarantees that for all .[ eg : popular ] consider a system with popular files .a possible evolution of the set of popular files is as follows . : : :  the initial set of popular files is . : : :  there is an arrival .the file is randomly chosen and  replaced with the new file , so that   . : : :  there is no arrival , and .we start by introducing a new , online , coded caching algorithm in section [ sec : main_algo ] .a simplified variant of this algorithm is shown in section [ sec : main_theory ] to have performance close to the optimal online caching scheme .section [ sec : main_sim ] provides simulation results comparing the proposed coded caching algorithm to the baseline lru scheme for an empirical demand time series derived from the netflix prize database .   in this section ,we propose an online version of the caching algorithm in , which we term _ coded least - recently sent _ ( lrs ) .the coded lrs algorithm is presented formally in the listing algorithm [ alg:1 ] .the statement of the algorithm uses the shorthand $ ] for .[ alg:1_sloop ] [ alg:1_sloop ] server sends [ alg : send ] user replaces the least recently sent file in its cache with a random subset of bits of file [ alg:1_cache ]  algorithm [ alg:1 ] consists of a delivery procedure and a cache update procedure .we now explain those two procedures in detail .the delivery procedure is formally similar to the delivery procedure of the decentralized caching algorithm in . denotes the bits of the file requested by user cached exclusively at users in . in other words , a bit of file is in if it is present in the cache of every user in and if it is absent from the cache of every user outside .the xor operation in line [ alg : send ] is to be understood as being applied element - wise to treated as a vector of bits .if those vectors do not have the same length , they are assumed to be zero padded for the purposes of the xor .we thus see that the delivery procedure of the coded lrs algorithm consists of sending one linear file combination for each subset of users .it is worth pointing out that , whenever a requested file is not cached at any user , then is equal to the entire requested file , and hence when in line [ alg:1_sloop ] the delivery procedure sends in this case the entire requested file uncoded over the shared link .consider next the cache update procedure . in each time slot , the users maintain a list of partially cached files for some .the parameter can be chosen to optimize the caching performance ; a simple and reasonable choice is . at time , after the delivery procedure is executed , the caches are updated as follows .if a requested file of _ any _ user is not currently partially cached , _ all _ users evict the least - recently used file and replace it with randomly chosen bits from file .this is feasible since the uncached file was sent uncoded over the shared link during the delivery procedure .note that this update procedure guarantees that the number of partially cached files remains , and that the same files ( but not necessarily the same bits ) are partially cached at each of the users .we illustrate the proposed coded lrs algorithm with an example .this example also illustrates that the rate of the proposed scheme can be related to the rate defined in  of the decentralized caching algorithm from  .we consider again a system with popular files and assume the same popular - file dynamics as in example [ eg : popular ] in section [ sec : problem ] .assume there are users with a cache memory of .let so that each user caches a fraction of files .we assume that initially each user partially caches the files . : : :  the set of popular files is .assume  the users request .both of the requested  files are partially cached at the users . in the delivery procedure,  the server sends , ,  and . for large enough ,so  that each of these file parts has close to expected size ( as discussed  in example [ eg : dec ] in section [ sec : background ] ) , this results in a  rate of   with   as defined in .since all the requested files  are already partially cached , the set of cached files stays the same  in the cache update procedure .in other words , each user still  partially caches . : : :  the set of popular files changes to . assume the users request   . here , file is partially  cached at the users but file is not .the server sends   , , and   .since is not cached at  any of the users , we have in this case that   and .hence , the transmission of the server is  equivalently , and   .this results in a rate of    since is the least - recently sent file , it is evicted  from each cache and replaced by a random third of the file   .the new set of partially cached files is   . : : :  the set of popular files stays the same .assume the users request   , both of which are now partially cached at  the users .the server now sends ,   , and . unlike the  previous time step , is now no longer empty , and the  resulting rate is as calculated  before .the set of partially cached files stays the same , namely   .it is worth comparing the proposed coded lrs algorithm with the well - known lru algorithm described in example [ eg : lru ] in section [ sec : problem ] .both of them are online algorithms . however , there are three key differences .first , coded lrs uses a coded delivery procedure whereas the transmissions in lru are uncoded .second , coded lrs caches many ( ) partial files whereas lru caches fewer ( ) whole files .third , coded lrs uses a least - recently sent eviction rule , taking into account the files requested by all users jointly , compared to the least - recently used eviction rule , taking into account only the files requested by every user individually .the impact of these differences will be explored in more detail later .the main result of this paper is the following theorem .[ thm1 ] the long - term average rate of the optimal online caching scheme satisfies where   the proof of theorem [ thm1 ] is presented in section [ sec : proof1 ] .the upper bound in theorem [ thm1 ] results from the analysis of a simplified version of the proposed coded lrs caching scheme , showing that this algorithm is approximately optimal .for the lower bound , we use the rate of the optimal offline scheme , whose rate is approximately .the theorem thus implies that the rate of the optimal online caching scheme is approximately the same as the rate of the optimal offline scheme .recall that in an offline scheme , the cache memories are given access to the entire set of popular files each time it changes .moreover , these cache updates are performed offline , meaning that the data transfer needed to update and maintain the caches is not counted towards the load of the shared link .in contrast , in the online scenario , caches are updated based on the limited observations they have through the sequence of demands . moreover , the cache updates is performed through the same shared link , and therefore affects the average rate .theorem [ thm1 ] thus indicates that these significant restrictions on the online problem have only a small effect on the rate compared to the offline scheme .popular files , users , and arrival probability .the figure plots the long - term average rate over the shared link as a function of cache memory size for lru ( dashed green ) , uncoded lrs ( dashed black ) , and the proposed coded lrs ( solid blue ) . ]we now compare the proposed coded lrs scheme to the baseline lru scheme .the performances of these two schemes are shown in fig .[ fig : synthetic ] for a system with popular files , users , and arrival probability . as is visible from the figure , coded lrs provides significant gains over lru both for small and large memory sizes . for example , for ( meaning that the cache is large enough to hold of the popular files ) , lru results in a rate of ( meaning that we need to send the equivalent of files over the shared link on average ) , whereas coded lrs results in a rate of .similarly , for , lru results in a rate of , whereas coded lrs results in a rate of .as mentioned in section [ sec : main_algo ] , the three main differences between coded lrs and lru are coded delivery , partial caching , and lrs eviction . to get a sense of the impact of these three differences , fig .[ fig : synthetic ] also depicts the performance of the uncoded lrs scheme . in this scheme , whole files are cached and uncoded delivery is used ( as in lru ) , however the lrs eviction rule is used ( unlike in lru ) .  comparing ( uncoded ) lrs to lru, we see that the two schemes perform quite similarly for small and moderate values of , say . for large values of ,say , lrs provides a significant improvement over lru .this is because when is close to the number of popular files , the rate is dominated by the arrival of new popular files , and lrs eviction allows the caches to learn these new files with fewer cache misses than lru .  comparing uncoded lrs to coded lrs , we see that only when is very close to the number of popular files are the performances of the schemes similar . for all other values ,coded lrs significantly outperforms uncoded lrs .this implies that , except for large values of , the main gain of the coded lrs scheme derives from the partial caching of many files and from the coded delivery .   to validate the theoretical analysis in section [ sec : main_theory ] as well as our model for the evolution of popular files, we now evaluate the performance of the proposed coded lrs and the baseline lru schemes for a real - life time series of demands .this time series is derived from the dataset made available by netflix for the netflix prize as follows .each entry in the netflix dataset consists of a user i d , a movie i d , a time stamp , and a rating that the user gave to the movie at the specified time .we are not interested in the rating here , but would like to use the time of rating a movie as a proxy for the time of viewing that movie .this approach is problematic for old movies , which users may rate long after they have seen them .however , it is reasonable to expect that the rating time is close to the viewing time for recently released movies . to ensure that this is the case , we selected all user ratings in the database from the year 2005 ( the last full year for which ratings are available ) , and kept only those that are for movies released in either 2004 or 2005 .the resulting filtered time series contains about user ratings for unique movies .    to validate this approach , fig .[ fig : troy_treasure ] plots the number of ratings for the two most - rated movies ( `` troy '' and `` national treasure '' ) as a function of time measured in weeks .the movie `` troy '' was released on dvd on january 4 , 2005 ( at which time it was likely also available on netflix ) , corresponding to week 1 .the movie `` national treasure '' was released on dvd on may 3 , 2005 , corresponding to week 18 .as can be seen from fig .[ fig : troy_treasure ] , the number of ratings increases strongly on the dvd release week , stays relatively high for a number of weeks , and then drops .this suggests that the rating time is indeed a valid proxy for the viewing time when applied to recently released movies .it also suggests that the model of time - varying popular files described in section [ sec : problem ] and used for the theoretical analysis in section [ sec : main_theory ] is a reasonable model for the viewing behavior of users .the figure plots the long - term average rate over the shared link as a function of cache memory size for lru ( dashed green ) and the proposed coded lrs ( solid blue ) . ][ fig : netflix ] compares the performance of the proposed coded lrs scheme to the baseline lru scheme for the netflix demand time series for a system with caches ( each in this case corresponding to many users that are attached to it ) .as is visible from the figure , coded lrs again significantly outperforms lru .in particular , for a cache size of , lru achieves a rate of compared to a rate of for coded lrs .to prove theorem [ thm1 ] , we establish an upper bound ( section [ sec : proof1_upper ] ) and a lower bound ( section [ sec : proof1_lower ] ) on the optimal long - term average rate .   for the upper bound on , we analyze a simplified version of the proposed coded lrs scheme .we refer to this simplified scheme as _ coded random eviction_. in coded random eviction , if files are requested by users at time that are not currently partially cached , then of the cached files are randomly chosen , evicted from _ all _ cache memories , and replaced with randomly chosen bits from each of the newly requested files .observe that this guarantees that the same collection of files is partially cached at each user .the remainder of the algorithm is the same as coded lrs as listed in algorithm [ alg:1 ] .in particular the coded random - eviction algorithm partially caches files for a positive constant at each user , where is the cardinality of the set of popular files .recall that , according to the system model described in section [ sec : problem ] , at each time slot , the users request randomly chosen files from the set of popular files without replacement . at any time , not all files in may be partially cached at the users . as in the previous paragraph , we denote by the ( random ) number of uncached files requested by the users at time . by definition, takes value in set .  the delivery procedure in algorithm [ alg:1 ]transmits these files uncoded over the shared link . to send the remaining files that are partially cached at the users , the delivery procedure of algorithm [ alg:1 ] uses codingthis requires a rate of as described in section [ sec : background ] , and with as defined in theorem [ thm1 ] and in .thus , the rate over the shared link at time is   the long - term average rate of coded random eviction is therefore upper bounded by to prove theorem [ thm1 ] , we show that the first term in  is approximately and that the second term is upper bounded by a constant .this second upper bound is perhaps surprising , since itself can take any value up to and is hence not upper bounded by a constant independent of the problem parameters .we start with the analysis of the second term in .let the random variable denote the number of files in that are partially stored in the caches at the beginning of time slot .note that takes value in .conditioned on , the random variable has expected value therefore , in what follows , we investigate the random process .[ thm : ergodic ] is a markov process and has a unique stationary distribution .moreover , where is distributed according to .  due to the nature of the random - eviction algorithm , and due to the memoryless arrivals and departures to the set of popular files , is a markov process .it is easy to see that this markov process has a single ergodic recurrent class consisting of the states and has transient states .therefore , has a unique stationary distribution .  from fubini s theorem and the properties of , we have since by ergodicity , we obtain from the cesro - mean theorem that this implies that completing the proof .  applying lemma [ thm : ergodic ] to  yields that to establish the upper bound on theorem [ thm1 ], it thus remains to lower bound .this is done in the next lemma .[ thm : quad ] let be as in lemma [ thm : ergodic ]. then   to analyze , we will need a more detailed understanding of the random process .we define two auxiliary processes , and , both for . is the number of randomly evicted files from the caches at the end of time slot that are in . in other words, counts the number of wrongly evicted files . is the indicator random variable of the event that , at the end of time slot , there is a departure from the set of popular files and that the departing file is partially stored in the caches at the end of time slot ( i.e. , after the cache update ) .  using these auxiliary processes , we can write the following update equation for process : in words ,  states that the number of correctly cached files at time is equal to the number of correctly cached files at time , plus the number of newly requested and cached files , minus the number of wrongly evicted files , minus the number of files that were correctly cached at the end of time slot but are no longer popular at time .[ eg : update ] consider a scenario with users and files .let and assume at time the files are partially cached .then , since the overlap is file .assume the users request at time .then , since two uncached files and are requested . to accommodate the two new files , we randomly evict two cached files .assume those files are and so that the cached files at the end of time slot are .then , since file in is evicted from the caches .finally assume that file is randomly selected to depart from and is replaced by the new file , so that . then , since the departed file is cached at the end of time slot .finally , , since file is both popular and cached .this satisfies   to establish a lower bound on we use the update equation  instead of directly computing the stationary distribution , which is not tractable .assume that the process is started in steady - state .in other words , has distribution for every .then , taking expectations on both sides of , since , this simplifies to   we now calculate the two expectations in .we start with the left expectation .consider the number of correctly cached files at the end of time slot just after the caches are updated but before any departures from the set of popular files .note that conditioned on , since a departure happens with probability and since there are files out of which are popular .now , so that solving for yields   we then consider the right expectation in . conditioned on and , the random variable has expected value since files are evicted and of the partial files in memory are correctly cached .thus , and finally , the right expectation in  can be evaluated as   for ease of notation , define substituting  and  into and rearranging yields then   this is a quadratic equation in the expected value of . in appendix[ sec : appendix_quadratic ] , we show that the solutions to this quadratic equation can be lower bounded as observe that , crucially , this lower bound does not depend on the variance of . using this lower bound on , we obtain after some algebra , concluding the proof of lemma [ thm : quad ] .applying lemma [ thm : quad ] to  and substituting into  shows that in appendix [ sec : appendix_ineq ] , we show that is upper bounded as , for .hence , setting , we obtain for , on the other hand , for , we trivially have   since the long - term average of the optimal scheme is less than or equal to , this implies concluding the proof of the upper bound in theorem [ thm1 ] .we consider a offline scenario in which all cache memories are fully aware of the set of popular files .in addition , at the beginning of each time slot , before users decide on their requests , the caches are given full access to all the files in to update their stored content at no cost .however , the cache memories are not aware of future requests . clearly , the rate of the optimal scheme for this offline setting is a lower bound on the optimal rate for the online setting .this offline problem is in fact equal to the prefetching problem investigated in  , where it is shown that the instantaneous rate , and therefore also the long - term average rate , is lower bounded by .thus , as needed to be shown .set then , can be written as with solutions . since is the average of a real random sequence andsatisfies the above quadratic equation , this equation has real solutions . in this case , the smaller solution is with the negative sign .thus , where for the last inequality we have used that .assume first that .then where the last inequality holds since for and .assume then that .then combining those two inequalities shows that

Abstract: we consider a basic content distribution scenario consisting of a single origin server connected through a shared bottleneck link to a number of users each equipped with a cache of finite memory . the users issue a sequence of content requests from a set of popular files , and the goal is to operate the caches as well as the server such that these requests are satisfied with the minimum number of bits sent over the shared link . assuming a basic markov model for renewing the set of popular files , we characterize approximately the optimal long - term average rate of the shared link . we further prove that the optimal online scheme has approximately the same performance as the optimal offline scheme , in which the cache contents can be updated based on the entire set of popular files before each new request . to support these theoretical results , we propose an online coded caching scheme termed _ coded least - recently sent _ ( lrs ) and simulate it for a demand time series derived from the dataset made available by netflix for the netflix prize . for this time series , we show that the proposed coded lrs algorithm significantly outperforms the popular least - recently used ( lru ) caching algorithm .


the central silicon tracker ( cst ) of the h1 experiment at the hera electron - proton collider of desy has been built to provide vertex information from precision measurements of charged particle tracks close to the interaction point .it consists of two concentric cylindrical layers of silicon sensors with two - coordinate readout allowing the identification of heavy - flavour particles with decay lengths of a few hundred micrometers .the production cross section for charmed quark pairs at hera is of order 1 which offers a rich field of physics topics that can be exploited once a large number of charm events are tagged by the vertex detector .in addition , the production of -quarks can be studied .the cross section is smaller by about two orders of magnitude but the longer lifetimes of b - mesons lead to a more efficient tagging .the bulk of the heavy quarks are produced close to threshold such that their decay products have an average transverse momentum around 0.7 gev / c . the vertex resolution is dominated by multiple scattering and the amount of material in front of the second silicon layer must be kept at a minimum .this led to a design with all readout electronics arranged at the ends and a central region consisting essentially only of active sensor material .space for the installation of the cst was obtained by reducing the beam pipe radius from 95 mm to 45 mm , which was the minimum radius required to protect the vertex detector from the direct and backscattered synchrotron radiation emitted by the electron beam .the cst has been fully operational since the beginning of the 1997 running period .it complements the original central tracking detectors of h1 , which consist of the main jet - cell drift chamber extending from 20.3 cm to 84.4 cm in radius , interspersed by a drift chamber for z - coordinate measurement between 46 cm and 48.5 cm radius , and an inner z - drift chamber between 17.35 cm and 20 cm radius .a superconducting coil provides a uniform magnetic field of 1.16 t .further details can be found in .simultaneously to the implementation of the cst the tracking of electrons scattered at small deflection angles was made possible with the installation of initially four and , since 1998 , eight disks of silicon sensors in the backward silicon tracker ( bst ) .the bst uses the same frontend asics and the same readout electronics as the cst .  in the following section the layout and mechanics of the cstare described .section 3 covers the frontend components , i.e. the sensors , the readout and control chips , the hybrid and the optical link .the on - line data processing and monitoring of slow control data is covered in section 4 .the off - line track linking and the alignment procedure are explained in section 5 .the performance numbers achieved so far are presented in section 6 .-plane.,height=453 ]  the radial space available for upgrading the h1 experiment with a vertex detector was limited on the outside by the first mwpc trigger chamber starting at 15 cm radius . on the insidethe space was restricted by a beam pipe radius of 4.5 cm as required by the synchrotron radiation environment , and by an additional 7 mm wide gap for cooling of the beam pipe with nitrogen gas flowing inside of a mylar foil .the beampipe was initially made of aluminium with a wall thickness of 1.7 mm .it was replaced in early 1998 by a beam pipe made of 0.15 mm aluminium and 0.9 mm carbon fiber .the two layers of the cst are formed from 12 and 20 faces at radii of 5.75 cm and 9.75 cm , respectively , as shown in figure [ r - phi ] .one face or laddder consists of six silicon sensors and aluminium nitride hybrids at each end ( see figure [ sideview ] ) .a double layer of carbon fiber strips with a total thickness of 700 m and a height of 4.4 mm is glued to the edges .the carbon fiber strips were specified with a young s modulus of at least 400000n / mm .the gravitational sag of a full ladder when supported at the outer ends was measured to be less than 6 m .the positions of the ladders in a layer are shifted tangentially to ensure an overlap in r- of adjacent active areas , which amounts to 1.5% in the inner layer and 2.1% in the outer layer .the active length in is 35.6 cm for both layers , see figure [ sideview ] , to be compared to the length of the luminous region at hera with an rms width of 10 cm .the coverage of the outer layer extends over units in pseudorapidity for tracks emerging from the origin .the length is a compromise between rapidity coverage and preamplifier noise which is proportional to the length .the ladders are mounted on small balconies extending from carbon fiber endflanges ( see figure [ end - flange ] ) .these balconies contain a high precision metal pin used to position the hybrids at laser - cut holes .two small screws on each hybrid are used for fixation .    the carbon fiber endflanges house a circular cooling water pipe for each layer with copper - tin sheets attached which reach into the balconies and thus provide thermal contact with the hybrids .the power dissipation of the cst is 50 w .this power is removed with 12 cold water at a total flow rate of 2/min .the equilibrium temperature rises from 19 for the unpowered detector to 28 during operation .the endflanges are split in the horizontal plane ( see figure [ end - flange ] ) allowing for the installation around the beam pipe .the lower half of the cst rests on three carbon fiber legs in a carbon fiber support tube ( see figure [ adapter ] ) which is attached to the innermost tracking chamber of h1 .the upper half of the cst rests on the lower half .    upon installation the two halves of the cstare first mounted on rail extensions around the beam pipe about 2 m from the final position .a split service tube enclosing power leads , optical fibers and cooling pipes is equally mounted behind the cst and connections between the cst and the service tube are made .then the cst and the service tube slide on straight carbon fiber rails , integrated in the support tube , into the final position , which is defined by spring - loaded end stops .the service tube , depicted in figure [ adapter ] , has a radial width of only 2 mm and surrounds the backward silicon tracker .the wall of the service tube is made of a sandwich of 20 m aluminium foil , 2 mm rohacell with grooves for the aluminium power leads and another 20 m aluminium foil . at the edges of the half - shells flat cooling pipes of 2 mm height are incorporated .cable connectors and voltage regulators are integrated in the service tube endflange facing away from the cst .each ladder consists of two electrical units , called half - ladders .a half - ladder consists of three silicon sensors of 300 m thickness , and a ceramic hybrid of 635 m thickness carrying the front - end electronics , see figure [ half - ladder ] .the silicon sensors have 12 m wide strip implants on both sides .the strips on the p - side , where holes are collected , are oriented parallel to the beam direction and have a pitch of 25 m .every second strip is read out for a measurement of the -coordinate at a known radius .the intermediate strips contribute to the signal by capacitive coupling and improve the position resolution .the implants on the n - side , where electrons are collected , are rotated by 90 with respect to the p - side strips and have a pitch of 88 m for a measurement of the z - coordinate .every n - strip is read out by means of a second metal layer integrated on the sensors .there are 640 readout lines on each side of a sensor , which are daisy - chained by aluminium wire bonds between sensors , and connected to preamplifier asics on the hybrid .this arrangement leads to an effective strip length of 17.3 cm on the p - side and to a three - fold ambiguity for the z - coordinate on the n - side .the insensitive region at each end of the sensors and a gap of 300 m between the sensors lead to a coverage in the z - direction of 97% on the p - side and 95% on the n - side . in total, the cst contains 64 half - ladders with 192 silicon sensors and 81920 readout channels .high resistivity n - type silicon ( cm ) was obtained as a 100 mm diameter boule from wacker chemitronic .cutting of 300 m wafers and polishing of both sides was performed by siltronix .the wafer processing was performed at csem , where the basic double sided process was extended to provide a second metal layer over a 5 m thick deposited oxide on the n - side .the contact vias between metal-1 and metal-2 have a drawn opening of and proved to be very reliable . using contact chain test structures a failure rate of less than was determined ( all cst sensors together contain vias ) .the masks for the 14 layers in this process were designed by the collaboration .the cst sensors have a full size of , such that two sensors can be produced on a 100 mm diameter wafer .the strip implants are dc coupled to the metal-1 layer on both sides .early prototypes were ac coupled but showed a defect rate for the coupling capacitors on the n - side that led us to resort to dc coupling .the intermediate strips on the p - side are biased from a common guard ring across a punch - through gap covered by a foxfet gate . with gate and guard at ground potential and positive bias voltage applied to the n - sidethe intermediate strips float at 4v , with a uniformity of about 1v on individual detectors and also between different wafers and different production lots .we are currently not supplying a dedicated gate voltage , although this option is available in the cabling scheme .the active area on the p - side ( the junction side ) is surrounded by a multi - ring guard structure with floating gates , that leads to a gradual increase of the surface potential from 0v at the innermost guard ring to the full bias voltage at the edge .the carbon fiber strips glued to the sides of the sensors are floating at bias potential .each strip on the n - side is surrounded by a narrow ring of p - implant to provide the necessary interstrip insulation .the n - side can only be operated at full depletion , which requires between 30v and 50v for the installed sensors .although the strips are dc coupled to the metal-1 layer and all n - side strips are read out we kept the accumulation channel structure which provides a high resistance connection to a common guard ring .the sensors can then be fully depleted for a measurement of the total leakage current with only 2 test probe contacts , instead of having to contact 640 strips on each side .detectors with less than 6 of leakage current at 50v bias where selected .further tests prior to assembly included sparse measurements of the punch - through voltage on the p - side and the conductivity of the metal-1 to metal-2 vias on the n - side .the depletion voltage was determined at several positions on each sensor by a measurement of the interstrip resistance on the n - side .finally , each sensor was scanned under a microscope for shorts or interrupts in the metallization .sensors with more than 6 defective strips on either side were rejected .the final yield of accepted sensors was 62% for 9 production lots .the interstrip capacitance of one strip with respect to its six closest readout neighbours was measured as 1.5pf / cm on the p - side , for 50 m pitch and 12 m implant width . on the n - sidea value of 19pf was measured for the capacitance of one strip with respect to the other 639 strips on a sensor .it is dominated by the overlap capacitance between metal-1 and metal-2 lines across the 5 m oxide layer .the time between bunch crossings at hera is 96ns while the h1 level-1 trigger decision arrives after 2.4 .therefore all front - end readout systems have to store the signals from at least 25 beam crossings in a pipeline . for the h1 silicon detectors an integrated preamplifier and pipeline chip with multiplexed readout for 128 channels has been developed and fabricated in 1.2 m cmos technology .figure [ apcschematic ] shows the schematics of the apc128 readout chip .the various external signals , internal switches and circuit components are explained in the following sections .the charge sensitive input amplifier consists of a single push - pull inverter stage which offers minimal noise for a given power dissipation .the open loop gain is about 150 , which , together with a ( parasitic ) feedback capacitance c , leads to a miller capacitance that is not much larger than the input load capacitance , especially on the n - side .the equivalent noise charge was measured as at 0.3mw power dissipation and sampling at 10mhz .the risetime of the amplifier with the detector load was measured to be 100ns for the p - side and 150ns for the n - side .due to dc coupling between sensor and chip the preamplifier must absorb the strip leakage current through its feedback resistor ( ) , which is adjustable by an external voltage and set to a value of about 1m .consequently the signal decay time is 450ns which is sufficient to avoid pile - up at hera .leakage currents of up to several hundred na per strip can be tolerated before the preamplifier runs into saturation .several switches are used to control the preamplifier . during data taking the input select switchis is closed , connecting the preamplifier input to a strip .the reset switch is open and the switch r12 is closed , activating the feedback resistor rg . by closing switch cs a second feedback capacitor c be added , which can be used for analog signal processing and calibration purposes . at h1 , however , this feature is not used during regular data taking .the sample / read switch sr connects the preamplifier output to the switched capacitor analog pipeline .the preamplifier can be tested by applying a voltage step to the cal input .the cal pulse is reduced internally by about a factor 35 ( not shown in figure [ apcschematic ] ) .the cal capacitors of four neighbouring channels have nominal values of 40 , 80 , 120 and 160ff , which leads to a charge injection corresponding to one to four minimum ionizing particles in 300 m of silicon for a 3v external test pulse .the output voltage of the preamplifier is captured on one of 32 capacitors ( ) that form the analog pipeline for each channel .the capacitors are cyclically switched under the control of a common shift register operating at the hera frequency of 10.4mhz .a sample clock made from two signals ( and ) , phase shifted by 50% , with flat tops and common low periods of at least several ns is required .the shift register is cleared by setting both clock signals high and requires a couple of nanoseconds per cell . the sample bit ( )must be refreshed externally every 32 cycles .the pipeline is stopped externally at a level-1 trigger signal .the h1 second level trigger may reject an event after a decision time of 22 , upon which the sampling phase is resumed .an l2 accept decision starts the readout , for which the apc must be put into a different mode .first , the input is disconnected from the silicon sensor by opening the input select switch is .this automatically closes the switches which connects all 128 strips to an extra preamplifier in auto - feedback configuration to absorb the leakage current during the readout phase .secondly , the sample / read switch sr is opened , and the switches are closed , which disconnects the write lines to the pipeline capacitors and prepares the read lines .thirdly , the reset switch is closed for a few to bring the preamplifier into a well - defined state .the apc employs a self - re - reading architecture where the pipeline capacitors are read back by the same preamplifier that wrote them .the pipeline cell associated with the triggered event is reached by advancing the sample bit in the shift register from the stopped position , refreshing it externally , if necessary .the sample enable bar switch seb is open during this phase in order not to discharge the pipeline capacitors while advancing the sample bit .the selected capacitor is then read back through the preamplifier by closing seb .the charge stored is amplified by a factor and copied to the latch capacitor c . a second and a third sample of the pulse stored in the pipelineis also read back and added to the charge on c , which improves the signal - to - noise ratio by effectively increasing the integration time .the latch capacitors are necessary to separate the preamplifier section of the apc , which operates at a voltage of about 2v ( v ) , from the readout section , that operates at 5v ( v ) .they also provide intermediate storage of the signals during the serial readout .thirdly , they are used to perform an on - chip pedestal subtraction . during sampling and up to this point the right plate of the latch capacitor c was connected to the readout amplifier by closing the latch enable switch le and permanently filling the readout shift register .switch le is now opened , which captures the signal charge on the right plate .the left plate is cleared by resetting the preamplifier .the pedestal is taken from three pipeline capacitors just before the event occurred and read back with the same procedure as the signal . with the r12 and reset switches open ,the preamplifier maintains the pedestal potential , including any shift of the operating point due to leakage current , at the left plate of c .when the readout amplifier is connected to c again the difference between pedestal and signal is transferred .the serial readout is controlled by a shift register which again requires a two - phased clock signal ( r and r ) and a readout bit rbi .the right plates of the latch capacitors c are sequentially connected to the readout amplifier having a feedback capacitance c , which provides an amplification of about 10 .a readout speed of 4mhz can be reached , if the analog output of the apc is immediateley followed by a driver amplifier .for the cst it is limited to 1.6mhz by the trace capacitance on the ceramic hybrid carrying the apc .the readout of 10 apcs is multiplexed by feeding the readout bit appearing at rbo to the rbi input of the next chip .a chip select mechanism ensures that only one apc at a time connects to the common readout line .the full serial readout cycle for 1280 channels requires 1.1ms , which is just sufficient in h1 .the apc requires 13 external signals , of which only the clock and sample bit signals are fast , while the others change only when switching from sampling to readout mode .the number of external clock and control signals that need to be brought to the front end can be reduced to four by using a dedicated decoder chip .the desired state of all apc switches is first loaded serially into registers on the decoder chip and then applied to the apc .the fast clock and data signals are passed directly either to the pipeline or the readout shift register .further functionalities have been added to the decoder chip : it can generate a test pulse for the signal at any of the 32 pipeline buffer positions .it has a 7-bit dac which drives a current source for the apc preamplifiers allowing to define the operating point externally . finally , two stabilized and one temperature dependent voltage can be connected to the readout line , which allows a gain calibration and temperature monitoring .the decoder chip was also fabricated in 1.2 m sacmos technology .aluminium nitride was chosen as the substrate of the ceramic hybrid for its excellent heat conductivity / km , compared to / km for aluminium oxide .the hybrids have a size of and have two conductor layers on each side .connecting vias and holes for fixing screws are cut by laser .one side contains a blank area of for heat contact with the mechanical support structure .five apcs and one decoder are mounted on each side of the hybrid and connected by aluminium wire bonds .the hybrid carries current sources for the apc preamplifiers , a voltage reference for gain calibration , a temperature monitor and drivers for the analog output signal .the back side of the hybrid , which supplies the n - side of the silicon sensors , is floating at bias voltage potential .the digital input signals are transferred across small capacitors which separate the dc levels .a thin kapton cable with 20 lines is glued and wire bonded to the hybrid and connects to a ring - shaped printed circuit board ( endring print ) mounted on the cst endflanges .the digital control signals and the analog readout are transferred by optical fibers over 34 m between the detector and the electronics trailer , which minimizes the amount of cable material introduced into the center of h1 and prevents electromagnetic interference .receivers for a set of four digital control signals are mounted on four endring prints , each serving one quarter of the cst .the analog signals are transmitted by a total of 64 leds , which are connected to sockets located on the endring print .one led transmits the serial readout of either 1280 p - side channels or 1280 n - side channels from two neighbouring half ladders .the leds for the n - side are floating at the bias voltage potential .the frontend system is connected via 34 m optical fibers and electrical cables to the readout electronics in the electronics trailer .the fibers and cables are interrupted twice by connector boards allowing the installation of the cst and access to other h1 detector components .figure [ readout ] shows schematically the components of the readout and monitoring system .all electrical and optical leads arrive at a converter card located in the electronics trailer .it contains led drivers for the digital control signals and pin diode receivers for the analog optical signals .it also provides passive filtering for the frontend supply voltages and the detector bias voltage .the supply voltages are further stabilized by active voltage regulators placed on the service tube about 1 m from the detector .these regulators can be adjusted from the converter cards allowing to optimize the working points individually for units consisting of pairs of ladders ( four half - ladders ) .finally , the converter cards include circuits for monitoring temperatures , voltages and detector leakage currents . if a given temperature limit is exceeded or if the cooling system fails , the converter card autonomously operates relays switching off the supply voltages to the frontend .the frontend voltages are generated in vme modules called onsiroc .the bias voltages are programmable in the range 0v to 108v .the onsiroc is interfaced to the h1 central trigger and generates the control sequences required to run the apc128 chips .a typical sequence occupies 32 kb in memory and is loaded through vme .a fast compiler was developed on a macintosh platform which allows to generate the sequences from higher level building blocks .the digitisation of the analog signals is performed on a custom - built pci - bus mezzanine card using 12 bit fadcs .the cst creates about 1 mb of raw data per event , which is transferred via pci bus into 8 mb memories on rio2 vme cards .a hit - finding and zero - suppression algorithm is executed on powerpc 604 risc processors operating at 96mhz .the algorithm first determines and subtracts an average baseline for groups of 128 channels located on individual frontend chips .the event - to - event variation of this common baseline is comparable to the single - channel rms noise . in a second loop over the data the individual pedestalsare subtracted and hit searching is performed .a hit is defined as a contiguous group of channels , each with an amplitude greater than its rms noise , and with an integrated pulse height of at least four times the average single channel noise .the hits are copied to an output buffer . in a third loopthe pedestals are updated , using a running average for each channel and each apc pipeline buffer , and variances for individual noise determination are accumulated , except for those channels contributing to a hit .further counters are used to identify hot channels which are included in the noise determination even if they contribute to hits , which eventually results in a higher calculated rms noise value with a corresponding reduction of efficiency .the hit finding algorithm executes in about 7ms with 10240 channels served by one processor , while the pedestal updating requires 10ms but is executed only every fourth event .the formatted hit data are sent via a vme - taxi optical link to the central data acquisition system of h1 .the apc128 chip has been tested for radiation sensitivity in a co source .a single chip can tolerate about 1kgy before the analog output saturates due to internal leakage currents .this limit is lower and depends on the readout speed when several chips are daisy - chained .all other front - end components have been selected for similar radiation tolerance .a set of silicon pin - diodes are attached to the outer shield of the cst .they are continously read out , independent of the h1 data acquisition system .the counting rate is monitored as a function of time and displayed in the h1 and hera control rooms . counting rates above a certain threshold require beam tuning or optimisation of collimator settings .if the conditions can not be improved within a few minutes the beams have to be dumped .this occurs a few times per year , mainly at the beginning of a running period .the dose determined by dosimeters attached to the cst was 50gy per year in 1996 and 1997 when hera stored positrons . during the electron running in 1998 a dose of up to 250gywas accumulated which led to severe base - line shifts in the apcs in the inner layer . in the 1999 shutdownthe affected ladders were moved to the outer layer and the readout ordering was changed to be fully efficient for the 1999 - 2000 running period .temperature dependent solid state current sources ( ad590 ) are mounted on the cst endflanges .they are directly monitored in the converter card which operates relays to cut off all supply voltages to the cst , should the temperature exceed a value of 60 .this hard wired safety circuit is independent of the h1 slow control system .furthermore the temperature reading is digitized and displayed by a labview application in the control room .each hybrid houses a voltage divider driven by a 2.5v voltage reference , one element being an ntc resistor for temperature measurement .furthermore a second reference voltage for gain calibration is derived from the same reference .the readout sequence directs the decoder chip to transfer these voltages over the analog readout chain at the end of each event readout .a monitoring program with access to the data stream samples and displays the temperatures and reference voltages and records their history .it also provides on - line hit - maps and pulse height distributions for immediate data quality control .tracks from the central tracking chambers are extrapolated to the cst half - ladders where the search region is limited to five units of the track extrapolation error .ambiguities due to multiple track fit hypotheses in the chambers are resolved by selecting the best combination of hits in the inner and outer cst layer .if several tracks cross one half - ladder they are sorted according to their extrapolation error and the best track is linked first .tracks are linked down to a separation of 150 m .the linking of n - side hits must resolve the three - fold ambiguity created by the daisy - chained readout with a spacing of 5.93 cm .tracks which have been measured in both z - chambers have extrapolation errors below 1 mm in z and are linked unambiguously . if only cjc information is available the resolution can be above 1 cm . for these cases the linking exploits the correlation between the inner and outer layer and uses the event vertex as a further constraint .the position and direction of a track can be determined from the hits in both projections and in both layers of the cst .together with the curvature measured in the cjc a so - called cst track can be defined .these tracks are used in the cst alignment and they provide a largely unbiased reference for a re - calibration of the cjc and the z - chambers .in order to profit from the high intrinsic position resolution of the cst the position of each sensor in space must be known with comparable precision .the alignment procedure consists of three steps : an optical survey for the three sensors on a half - ladder , an internal software alignment of the 64 half - ladders relative to each other and a software alignment of the entire cst relative to the rest of the h1 tracking system .each half - ladder was surveyed using a microscope and a step - motor controlled x - y stage with 1 m resolution .a z - coordinate perpendicular to the sensor plane was measured using the focal adjustment coupled to a digital micrometer .each sensor has 12 alignment marks on the metallization layer whose positions relative to the strip implants are known from the mask design and within processing tolerances of less than 3 m .the survey was analyzed in terms of the relative displacements and rotations of the three sensors on a half - ladder to an accuracy of 3 m and 0.1mrad .it was observed that the individual sensors are not perfectly flat but are curved with a sagitta of about 30 m over a diagonal .a common average curvature is used for all sensors in alignment and reconstruction .the original wafers were flat within 5 m after cutting and polishing .the curvature is probably caused by the thick oxide layer deposited on the n - side .the positions of the ladders are defined by the balconies on the carbon fiber endflanges .the mechanical precision of the balconies and the assembly procedure assure that no forces which may deform the ladders are exerted .the placement in space is accurate to a few hundred micrometers . after applying the alignment corrections from the optical surveythe 64 half - ladders are treated as rigid bodies , which require 384 alignment parameters .these are determined in a software alignment procedure using three sets of tracking data .gev / c and cm before and after alignment , height=340 ]  cosmic ray data are taken regularly during breaks in the hera machine operation .penetrating tracks with 4 hits in the cst are selected .the parameters of the upper and the lower track must agree within errors , which leads to four constraint equations . as an example figure [ mumiss ] shows the distribution of the difference of the track positions at their closest approach to the origin of the h1 coordinate system the so - called muon miss - distance .after alignment the standard deviation of the gaussian is 52 m , which corresponds to a single - track impact parameter resolution of 38 m for tracks with a transverse momentum above 4gev / c .the corresponding impact parameter resolution in the z - projection is 74 .several million cosmic ray triggers are required for a sufficient illumination of all half - ladders .projection after alignment.,height=340 ]  m pitch ) .strip 0 is next to the guard ring .the curve is a fit to a semi - gaussian with a width of 0.85 pitch units.,height=340 ]    cosmic tracks mainly constrain the relative positions of half - ladders in the inner and outer layer and in the upper and lower half of the cst .the position of neighbouring half - ladders are constrained by tracks passing through the overlap regions .tracks with 3 hits are selected from normal luminosity data and are used to formulate two constraint equations , one in each readout coordinate .two hits are used to define the track and to predict the hit in the overlap region .a distribution of residuals in the projection is shown in figure [ xres ] from which an intrinsic point resolution of 12 m is inferred .close to the guard ring region of the sensors a systematic shift of the overlap residuals is observed . in figure [ shift ] the mean of the residual distribution is shown as a function of the distance of the reconstructed cluster position from the guard ring .the shift is well described by a semi - gaussian with an amplitude of 33 m and a width of 0.85 pitch units .the shift is attributed to charge collected on the guard ring . a correction is made and overlaps on the first two strips are not used in the alignment procedure .the angles of incidence do not deviate by more than 22 from the normal in the projection while much larger angles occur in the projection .the dependence of the intrinsic z - resolution ( measured on the n - side ) on the angle of incidence is shown in figure [ zres ] .it is well described by a parabola and reaches a minimum of 22 m at 15 from normal incidence .multi - track events from data are selected and a common 3d event vertex fit is performed .the sum of the values over several ten thousand events is included in the overall minimization with respect to the alignment parameters .this method alone does not lead to a robust estimation of the internal alignment parameters but together with cosmic rays and overlap tracks it provides a uniformly distributed track sample of high statistics that improves the quality of the combined alignment .the alignment is performed using the three data sets simultaneously .a common is accumulated and minimized iteratively with respect to the 384 local alignment parameters .the sparseness of the corresponding hessian matrix is exploited for a fast solution of the linearized equations .two sets of alignment parameters were determined for 1997 , using alignment data sets taken several months apart .the parameters are made comparable by applying six overall constraints , that correspond to a displacements or rotation of the entire cst .it is found that the internal alignment parameters agree with rms spreads of 6 m and 0.1mrad .compared to the intrinsic silicon resolution this reproducibility and long - term stability is sufficient .the global alignment determines the displacements and tilts of the entire cst with respect to the cjc and the z - chambers .six parameters are determined by minimizing the differences between cst and cjc tracks , using events and cosmic rays .the on - line zero - suppression on average finds 60 p - side clusters and 200 n - side clusters , corresponding to channel occupancies of 0.8% and 2% , respectively .the higher occupancy on the n - side is due to larger non - gaussian tails in the noise distribution .the occupancies are stable in time .the average number of linked hits is 14 for each projection which represents the track - related occupancy .minimum ionizing particles have a most probable energy loss of 84kev in 300 m of silicon , which leads to a signal of about 23000 electron - hole pairs .the thermal noise level is determined by the preamplifier design , its operating conditions and the detector load capacitance . for three daisy - chained sensorsthe capacitance of one strip to all neighbours amounts to 27pf on the p - side and 57pf on the n - side , where the contribution from the double metallization dominates .the apc is routinely operated in a triple sampling mode and with a power dissipation of 0.3mw per channel .figure [ landau - p ] shows the distribution of cluster pulse heights divided by the average single - channel noise for cosmic muon tracks , normalized to vertical incidence . the shape is well described by a landau energy loss distribution with a most probable signal - to - noise ratio of 19 for the p - side and 6.7 for the n - side , see figure [ landau - n ] .the difference is due to the strip capacitance loading the preamplifier which is a factor of two larger on the n - side , and due to the incomplete charge amplification caused by the limited gain of the preamplifier .the cst hit efficiencies are most accurately determined with cosmic tracks passing through four cst half - ladders . using three linked hits and the curvature from the cjcthe track parameters are determined in a fit and the intersection with the fourth half - ladder is calculated .figure [ tzhr ] shows for a sample of 20000 muon tracks with transverse momentum above 2gev the distance between the intersection point and all hits in the test layer in the z - projection .the central peak at zero contains the signal hits while the noise hits create a flat background distribution .the central peak can be described by two gaussians with widths of 33 m and 64 m for test half - ladders in the inner and outer layer , respectively . by comparing the number of hits in the peak with the number of passing tracks one can determine the hit - efficiencies .[ hit - eff ] shows the results for p- and n - side hits for all 64 half - ladders .    besides some fluctuations , which can be associated with specific hardware problems for the selected data runs , the efficiencies are in agreement with being the same for all half - ladders . for the p - sidethe average efficiency is 97% , while it is 92% for the n - side .the inefficiencies is caused by silicon defects , dead or noisy readout channels , the hit finding algorithm and the linking procedure .the lower efficiency for n - side is due to the lower signal - to - noise ratio .a precise knowledge of the beam position as a function of time is required for many decay - length or impact parameter studies .the beam position and tilt is determined by accumulating cst tracks over typically 30 minutes and minimizing the closest approach to a line in space .figure [ runvertex ] shows the horizontal and vertical beam position determined for the 1997 luminosity period .the horizontal beam movements reflect adjustments to the hera optics .the remaining distribution of the closest approach to the beam line ( ) has a central gaussian part with contributions from the cst intrinsic resolution , from multiple scattering in the beam pipe and the first silicon layer and from the beam spot size .the decays of long - lived particles contribute to the non - gaussian tails . from the hera machineoptics an elliptical beam spot with a horizontal - to - vertical aspect ratio of 5 to 1 is expected .this allows to separate the different contributions by measuring the width of the central gaussian of the distribution as a function of the track direction around the beam .the result is shown in figure [ beamspot ] for tracks with high momentum where the multiple scattering contribution can be neglected .   around the beam spot for transverse momenta above 4gev / c .the curve is discussed in the text.,height=340 ]  a fit of the form is used to extract the cst intrinsic resolution of m and a horizontal beam spot size of m , which agrees with the hera optics .a ratio as given by the optics was assumed in the fit to unfold the cst intrinsic resolution .   ) .the open symbols are from 1997 ( al beam pipe ) , the filled symbols from 1999 ( carbon fiber beam pipe ) .the curves are discussed in the text.,height=340 ]  the multiple scattering contribution to the width of the can be measured as a function of momentum by unfolding the contribution of the beam spot size .this contribution is minimal for horizontal tracks .the result is shown in figure [ dcares ] for data from 1997 and from 1999 .a fit according to leads to asymptotic values of m and m for the two years while the parameter improves by a factor 1.55 , as expected for the change from an aluminium beam pipe ( ) to a carbon fiber beam pipe ( ) , when adding the constant contribution of the first silicon layer and the cst inner shield .the h1 silicon vertex detector cst has been operated successfully at hera since the beginning of 1997 .the sensors , the readout electronics and the optical signal transmission are functioning reliably and efficienctly . a point resolution of 12 m with a signal - to - noise ratio of 19 has been achieved for the coordinate , while the minimal point resolution in is 22 m with a signal - to - noise ratio of 7 .an impact parameter resolution of 37 m in the plane has been achieved for high momentum tracks , which opens a wide range of physics topics in the field of heavy quark production in electron - proton collisions .99 i.abt et al . , nucl .instr . and meth .a386 ( 1997 ) 310 and a386 ( 1997 ) 348 h1 collaboration , technical proposal to build silicon tracking detectors for h1 , desy prc 92/01 , july 1992 ; r.horisberger , proc .europhysics conf . on high energy physics , marseille , july 1993 r.eichler and s.frixione , proceedings _ future physics at hera _ , hamburg 1996 , g.ingelmann , a.deroeck , r.klanner ( editors )w.eick et al .instr . and meth .a386(1997 ) 81 m.biddulph , phd thesis no eth-12331 , ( 1997 ) d.pitzl et al . ,instr . and meth .a348(1994 ) 454 wacker chemitronics , burgdorf , germany c.s.e.m .sa , ch 2007 neuchtel , maladire 71 , switzerland siltronix sa , ch-1214 vernier geneva , switzerland radeberger hybridelektronik gmbh , d-01454 radeberg , germany w.erdmann et al .instr . and meth .a372(1996 ) 188 j.buerger et al . , nucl .instr . andmeth.a386(1997 ) 269 w.j.haynes et al . , nucl . instr . and meth .a403(1998 ) 313 ces 8320 rio2 , creative electronic systems , geneva a prototyp version with 12 channels has been described in : r.horisberger and d.pitzl , nucl .instr . and meth .a326(1993 ) 92 faselec ag , philips semiconductor , binzstr .44 , ch-8045 zrich , switzerland .g.klaiber , diplomathesiseth - zurich 1996 , unpublished rohacell from roehm ag , switzerland j.gassner , diplomathesis eth - zurich 1996 , unpublished ljnsson , b.lundberg , u.mjrnmark , lund university , sweden v.blobel , private commuinication .see also http://www.desy.de//

Abstract: the design , construction and performance of the h1 silicon vertex detector is described . it consists of two cylindrical layers of double sided , double metal silicon sensors read out by a custom designed analog pipeline chip . the analog signals are transmitted by optical fibers to a custom designed adc board and are reduced on powerpc processors . details of the design and construction are given and performance figures from the first data taking periods are presented .