the following observations and derivations apply to an idealized betatron system whose consideration is helpful in the appreciation of preferred embodiments of the invention . in such an idealized system , magnet - excitation power conversion efficiency is optimized upon maximization of the beam end - point energy at a given level of magnet excitation energy . the betatron orbit , r 0 , is related to the total magnetic flux φ within r 0 and to the magnetic induction b at r 0 through the following relation , which is known as the betatron condition : where δ is a difference operator for an incremental change in time . to maintain a constant betatron orbit , the left - hand - side ratio must be kept constant . this is usually achieved with a technique known as flux forcing . the voltages applied to the field and core coils are related to the respective magnetic fluxes through the following relations : where c as a subscript refers to the core coil and f to the field magnet coil . v is the applied voltage , n the number of turns of the winding , i the corresponding driving current , r the effective magnet circuit resistance , b . the average magnetic induction , and a the cross - sectional area of the pole face . if the circuit is designed so that the left hand side of equation ( 6 ) is directly proportional to the left hand side of equation ( 1 ). the right hand side of equation ( 6 ) is simply a geometrical constant . as a result , the betatron condition is satisfied . when , due to a change in temperature , equation ( 4 ) no longer applies , the value of v c or v t may be adjusted to accommodate for the change . to this end , however , a simple parallel connection of the two coils is no longer sufficient . for example , if the magnetic circuit is designed for room temperature , and if the actual temperature rises , then a suitable increase of v c or reduction of v f will keep the betatron condition satisfied . because the energy associated with the core circuit is considerably less than the energy in the field circuit , changing v c requires less power , so that , in the interest of economy , changing v c is preferred . suitable voltage adjustments may be carried out interactively and continuously . in accordance with the present invention , a preferred voltage adjustment may be effected , e . g ., by modulator circuitry disclosed in the aforementioned u . s . pat . no . 5 , 077 , 530 , as suitably modified by the addition of &# 34 ; turbo - charge &# 34 ; circuitry , as illustrated in fig1 and 2 for example . shown in fig1 is a main discharging and energy recovery ( modulator ) circuit 1 of a type disclosed in the aforementioned u . s . pat . no . 5 , 077 , 530 . circuit 1 includes a direct - current , low - voltage power supply 18 , typically for supplying a voltage in the range of 10 to 100 volts . via a diode 24 , an isolation choke 22 , and a charging switch 23 , the power supply 18 is connected in parallel with a low - voltage storage capacitor 20 , as well as to the positive side of the field - coil winding 26 ( having inductance l 2 ) and , via a diode 40 , to the positive side of the core - coil winding 27 ( having inductance l 3 ). although the field - coil and core - coil windings are illustrated as separate windings in fig1 it will be understood that a single primary winding could be used to drive both the field magnet and the core magnet if desired . as described in u . s . pat . no . 5 , 122 , 662 , a secondary winding would then be used to provide the difference in magneto - motive force between the core and field magnets . charging switch 23 provides isolation for the power supply and may be implemented in the form of a bank of field - effect transistors , for example . in such implementation , in which field - effect transistors have intrinsic body diodes connecting source to drain , diode 24 prevents reverse current flow . diode 40 isolates the field - coil winding 26 from the core - coil winding 27 during activation of the turbo - charge unit described below . the negative side of the field - coil winding 26 is connected via a blocking diode 30 to a high - voltage storage capacitor 32 ( having capacitance c 2 ), and the negative side of the core - coil winding 27 is similarly connected to the capacitor 32 via orbit - compression switch 29 . this switch 29 is open during electron injection and closed during acceleration and expansion . the diode 34 isolates the capacitor 32 from ground . as will be appreciated , and as is described more fully in the aforementioned u . s . pat . no . 5 , 077 , 530 , the capacitor 20 , choke 22 and diode 24 form a low - voltage charging circuit for transferring energy through the field - coil winding 26 and the core - coil winding 27 to the high - voltage excitation circuit comprised by the diode 30 , capacitor 32 , and diode 34 . diode 28 is included to prevent reverse - charging of capacitor 20 , but may be omitted as redundant depending on betatron operating conditions . switches 36 and 38 permit , selectively , ( 1 ) current flow from the low - voltage capacitor 20 through the field - coil winding 26 and the core - coil winding 27 to the high - voltage capacitor 32 and ( 2 ) reverse current flow so as to discharge the combined charge of both capacitors 20 and 32 through the windings 26 and 27 and thereby excite the field - coil and core - coil circuits . in accordance with the invention , the main modulator circuit 1 is shown augmented by an embodiment 11 of a &# 34 ; turbo charge unit &# 34 ; for electron orbit control . unit 11 includes an additional high - voltage capacitor 42 ( having capacitance c 3 ) which is connected in parallel to the main energy storage capacitor 32 via a charging switch 44 and a charging diode 46 . in operation , the capacitor 42 is charged together with the main capacitor 32 ; however , the voltage of capacitor 42 is controlled by the switch 44 . during discharge , the energy stored in capacitor 42 is blocked by a switch 48 until the onset of orbit expansion , or when a shift in x - ray burst timing is detected by an x - ray timing sensing unit 50 . at that time , a timing control circuit sends the required trigger signal to switch 48 and releases the energy in capacitor 42 into the core - coil winding 27 . the voltage blocking diode 40 blocks the higher voltage across the core - coil winding 27 from the voltage across the field - coil winding 26 ; thus , the core - coil and field - coil discharging paths are isolated . the timing control circuit may raise or lower the voltage of capacitor 42 , or change its discharging timing as appropriate , to maintain the x - ray burst timing substantially constant . to prevent the turbo charge unit 11 from exhausting its energy before the electron beam strikes the target , the following condition is sufficient : this is not a necessary condition , however , as onset of the discharge of the capacitor 42 is delayed with respect to the discharge of the capacitor 32 . typically , the core - coil inductance l 3 is an order of magnitude larger than the field - coil inductance l 2 , representative values being l 2 = 85 μh and l 3 = 750 μh , with c 2 = 5 μf . thus , preferably , the capacitor 42 has relatively low capacitance c 3 , e . g . about 0 . 5 μf . however , it is important to bear in mind that the inductance l 3 of the core - coil winding 27 is inversely related to temperature , and that the capacitance c 3 of capacitor 42 should be selected such that , throughout an intended operating temperature range , the capacitor 42 does not fully discharge before beam extraction is complete . fig2 depicts an alternative circuit arrangement , including a main modulator circuit 2 and a turbo charge unit 21 with components analogous to those of units 1 and 11 of fig1 and interconnected as shown . like reference numbers are used to identify like parts . in the circuit in accordance with fig1 orbit control is effected by raising the voltage at the positive terminal of the core - coil winding 27 ; conversely , to the same effect , voltage is lowered at the negative terminal of the core - coil winding 27 in the circuit in accordance with fig2 . in both embodiments , the diodes 46 and 47 serve to block reverse current , similar to the function of diode 24 discussed above . such blocking is of particular importance with switches 44 and 48 including field - effect transistors . functioning of the turbo - charge unit may be appreciated in further detail with reference to the timing diagrams of fig3 and 4 , where the instances t , t 3 and t 5 are related to instances with the same designations in the aforementioned u . s . pat . no . 5 , 077 , 530 . as described above , the electron orbit is expanded when the voltage v c in accordance with equation 2 is raised above the voltage v f in accordance with equation 3 . the capacitor 42 is charged during the energy recovery period ( t 3 to t 5 ) upon closing of the switch 44 . if switch 44 remains closed for the entire energy recovery period , the voltage across the additional capacitor 42 is the same as the voltage across the main capacitor 32 , otherwise it is lower . the turbo - charge unit can be activated only after the voltage across the main capacitor 32 ( which is the same as the voltage across the field coil winding 26 and the core - coil winding 27 ) has dropped below the voltage across the additional capacitor 42 . otherwise , diode 47 blocks the energy in the additional capacitor 42 from being discharged . when the turbo - charge unit is activated by closing switch 48 , the voltage across the main capacitor 32 is imposed upon the core coil 27 . since this voltage is greater than the voltage across the field - coil winding 26 , the diode 40 is reverse biased and sustains the higher voltage across the core coil 27 for the remainder of the acceleration period . the core - coil current and the field - coil current follow separate paths after the activation of the turbo circuit : while the field circuit loop remains the same as before ( 26 - 36 - 32 - 38 - 20 - 26 ) the core circuit loop ( 27 - 29 - 36 - 42 - 48 - 27 ) goes through the turbo unit and bypasses the capacitors 32 and 20 . in fig3 v 3 represents the voltage to which the additional capacitor 42 is charged . this voltage waveform is obtained by subtracting the voltage at node 2 from the voltage at node 1 of fig1 . the voltage waveform over the core - coil winding is obtained by subtracting the voltage at node 3 from the voltage at node 1 of fig1 . the two wave forms overlap before the turbo circuit is activated . the acceleration period starts at t 1 and ends at t 3 , the energy recovery period extends from t 3 to t 5 . during the orbit expansion period between t 2 and t 3 , the voltage across the core coil is substantially higher than the voltage across the field coil . the turbo charging switch 44 is closed immediately following the opening of switch 48 , and remains closed until t 4 , at which time the voltage at capacitor 42 reaches v 3 . the cycle repeats thereafter . the trigger signals for the switches 44 and 48 may be generated in various known ways . since maintaining the x - ray burst near the peak of the current waveform ( or the minimum of the voltage waveforms -- see fig3 of u . s . pat . no . 5 , 077 , 530 ) is desirable for purposes of the present invention , an x - ray timing sensing unit 50 is preferably used to detect the timing of the electromagnetic radiation burst . this may be done , for example , by measuring the electromagnetic radiation burst by use of a gamma ray detector , such as a nai scintillator detector or other suitable detector , positioned close to the betatron . the peak of the burst is then determined and compared with a preset burst peak time location . circuitry for performing these functions is disclosed , for example , in u . s . pat . no . 4 , 972 , 082 , the pertinent disclosure of which is hereby incorporated by reference . an alternative technique for x - ray timing sensing may be described as follows : desired x - ray burst timing between t 3 &# 39 ; and t 3 , during which time interval the main switches 36 and 38 remain closed , is realized at essentially peak field - coil current . to this end , the time interval from t 3 &# 39 ; to t 3 , here designated as gate 2 , is a sliding gate of fixed width whose position is adjusted for peak field - coil current . with gate designating a suitable time interval ( of 10 μs duration , for example ) immediately preceding gate 2 , and gate 3 a suitable time interval ( also of 10 μs duration , for example ) immediately following gate 2 , integrating x - ray monitors for gates 1 , 2 and 3 ideally should read zero for gates 1 and 3 . in this case , the current position of gate 2 can remain unchanged . if the x - ray burst has shifted into gate 1 , the voltage of turbo capacitor 42 should be reduced by shortening of its charging time upon shifting t 4 to the left . conversely , if x - rays are detected in gate 3 , t 4 should be shifted to the right . standard circuitry and computer control can be used for such adjustment operations . with either technique , an error signal is generated that can be used to adjust the timing of the trigger signals to the switches 44 and 48 as required . if the x - ray burst is shifted to a later time , it can be moved back by either starting the electron beam orbit expansion at an earlier time ( shifting t 2 to the left in fig3 ) or by increasing v 3 ( shifting t 4 to the right in fig3 ). the invention is of particular commercial interest in borehole logging use and wherever small size and / or low power consumption are of concern in a betatron . thus , for example , the invention may be used in portable radiography units . although the invention has been described and illustrated herein by reference to specific embodiments thereof , it will be understood that such embodiments are susceptible of variation and modification without departing from the inventive concepts disclosed . all such variations and modifications , therefore , are intended to be included within the spirit and scope of the appended claims .