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MHD Simulations of Parker Instability Undergoing Cosmic-Ray Diffusion
Parker instability arises from the presence of magnetic fields in a plasma in a gravitational field such as the interstellar medium (ISM), wherein the magnetic buoyant pressure expels the gas and causes the gas to move along the field lines. The subsequent gravitational collapse of the plasma gas is thought to be responsible for the formation of giant molecular clouds in the Galaxy. The process of mixing in the ISM near the Galactic plane is investigated. The initial ISM is assumed to consist of two fluids: plasma gas and cosmic-ray particles, in hydrostatic equilibrium, coupled with a uniform, azimuthally-aligned magnetic field. The evolution of the instability is explored in two models: an isothermal exponential-declining density model and a two-layered, hyperbolic tangent temperature model. After a small perturbation, the unstable gas aggregates at the bottom of the magnetic loops and forms dense blobs. The growth rate of the instability decreases as the coupling between the cosmic rays and the plasma becomes stronger (meaning a smaller CR diffusion coefficient). The mixing is enhanced by the cosmic-ray diffusion, while the shape of the condensed gas depends sensitively on the initial equilibrium conditions. The hyperbolic tangent temperature model produces a more concentrated and round shape of clumps at the foot points of rising magnetic arches, like the observed giant molecular cloud, whereas the exponential density model gives rise to a filamentary morphology of the clumpy structure. When considering a minimum perpendicular or cross field diffusion of cosmic rays, which is often substantially smaller than the parallel coefficient , around of , the flow speed is significantly increased such that the magnetic loops extend to a greater altitude. We speculate that the galactic wind flow perpendicular to the galactic disk may be facilitated by Parker instabilities through the cross field diffusion of cosmic rays.
1 Introduction
Parker (1966) first identified the instability of a gravitationally stratified gaseous disk in a magneto-hydrostatic equilibrium, like the Galaxy, in response to perturbations due to magnetic buoyancy, for perturbations that occur in the magnetic field lines that lie parallel to the disk plane. This phenomenon is referred to as magnetic buoyancy instability (Hughes & Proctor 1988; Tajima & Shibata 1997) or Parker instability (Parker 1966; 1979). Solar magnetic activities such as sunspots, which is caused by the emergence of magnetic flux tubes from the interior of the sun into the solar atmosphere (Zwaan 1985, 1987), reflect this instability. The mushroom shape of the hydrogen cloud GW 123.4-1.5 (Baek, Kudoh & Tomisaka, 2008) also suggested magnetic flotation and, hence, Parker instability. In addition, giant dense CO molecular loops close to the Galactic center has been ascribed to the instability (Fukui et al., 2006). As is expected, gas aggregating at the foot points of the rising magnetic loops eventually collapses, becoming a giant cloud and a region that hosts stellar formations. On the other hand, for models galactic dynamos, Hanasz et al. (2004) found that if the effect of cosmic rays is incorporated, the efficiency of sustaining the galactic magnetic field can be improved. Otmianowska-Mazur et al. (2009) suggested that the extended, X-shaped magnetic halo structures observed in some edge-on galaxies could be attributed to the cosmic-ray driven dynamo. Actually, based on his instability, Parker (1992) introduced the idea of cosmic-ray driven dynamo to maintain the Galactic magnetic field, because the cosmic-ray pressure functions just like the magnetic pressure, capable of overpowering the gas pressure inside the magnetic flux tube and making it easier for the gas to rise.
Cosmic rays are a major component in the interstellar medium (ISM) in galaxies, whose energy density is comparable to the kinetic and magnetic energy densities of thermal plasma gas (Ferriére 2001). As high energy particles endowed with an energy of up to , of which, 90% are protons, as long as their gyroradius is significantly smaller than the characteristic spatial scales of the magnetic field, cosmic-ray particles only propagate along the magnetic field lines. When the gyroradius is comparable to the scale of magnetic field variation, cosmic rays interact strongly with the field through gyroresonant scattering by the magnetic irregularities. Although the velocity of cosmic-ray particles is close to the speed of light, the bulk motion of cosmic rays is diffusive and the bulk speed is of the order of Alfvén speed (Cesarsky 1980).
The morphology of Parker instability exhibits two modes, i.e. the undular mode and the interchange mode. The undular mode, also called Parker instability, is excited by perturbations along the magnetic field lines (the wavenumber vector of the perturbation parallel to the magnetic field ), where the falling gas creates a magnetic buoyancy greater than the restoring magnetic tension. The interchange mode, known as flute instability or magnetic Rayleigh-Taylor instability (Kruskal & Schwarzchild 1954), occurs for shorter-wavelength perturbations with perpendicular to , capable of causing two straight flux tubes to interchange and ultimately reducing the potential energy in the system. The linear growth rate of the interchange mode generally exceeds that of the undular mode owing to a rapid growth of short wavelengths. However, in the nonlinear stage, the undular mode often dominates (Matsumoto et al, 1993; Tajima & Shibata 1997). Thus, the undular mode (Parker instability) is more important than the interchange mode in astrophysical problems.
Baierlein (1983) and Matsumoto et al. (1988) performed the first one- and two-dimensional (2D), pure MHD simulations of Parker instability, respectively. In the nonlinear stage, the gas condensates to form giant clouds; in addition, a shock wave appears in the flow along the rising magnetic loop. By applying the simulation results of Matsumoto et al. (1988) to the solar atmosphere, Shibata et al. (1989b; 1990a) demonstrated that the emerging magnetic loop still expands self-similarly during the nonlinar evolution in two dimensions. Kamaya et al. (1996) adopted the supernova explosion as a perturbation in the ISM to trigger nonlinear instability. Earlier, Nozawa (1992) examined the instability deeper in the convectively unstable layer of the solar atmosphere; when considering how magnetic shear affects the flow (Hanawa et al. 1992, Nozawa 2005), although the interchange mode is stabilized, a large unstable thin structure may still arise. Shantanu et al. (1997) and Kim et al. (2000) made a further application of Parker instability to the Galactic disk without cosmic rays.
Parker's original analysis showed that the instability has a maximum growth rate for non-zero , although non-zero is the main cause for the instability. In the 3D simulations for both solar and galactic problems given in Matsumoto & Shibata (1992) and Matsumoto et al. (1993), previous 2D results of cloud formation, presence of shock wave, and self-similar evolution are confirmed. However, the spatial and temporal scale in these studies depends on the . If a larger is applied, the magnetic loop tends to have a thinner structure and a horizontal expansion, which would suppress the upward expansion (Parker 1979). Similarly thin slice structures have been found in other 3D simulations of Kim et al. (1998, 2001, 2001) and Hanasz et al. (2002).
This study describes the evolution of Parker instability undergoing cosmic-ray diffusion using 2D simulations. Effects of the adiabatic index and the initial hydrostatic condition other than an isothermal temperature and a uniform density profile are examined. Two initial profiles are used, i.e., the hyperbolic tangent temperature model, which is often used in the solar atmosphere, and the exponential density model, which is appropriate for Galactic problems. Various perturbation results are explored. The physical parameters and initial conditions invoked are appropriate for a galactic ISM in the solar neighborhood. Section 2–6 details the governing equations, numerical algorithms, normalization, initial conditions, and grid setup. Section 7 presents the results. Section 8 draws the conclusion.
2 Governing Equations
We investigate the Parker instability with respect to how cosmic rays affect the fluid element in a uniformly-rotating galactic disk, under the influence of external gravity from the galactic center. A local rectangular domain representing the corotating sheet of the disk in the vertical plane is used for the simulations. The horizontal component of the radially inward external gravity is balanced by the centrifugal force, and hence, in the momentum equation, only the vertical component of external gravity and the Coriolis force are present to account for the rotation. Self-gravity from the plasma gas is not included.
A hydrodynamic approach is adopted, in which the cosmic rays and the thermal plasma are two separate fluid components of a plasma system. The plasma fluid has a mass density of , a thermal pressure of , and a cosmic-ray pressure of , all of which are threaded by a frozen-in magnetic field . The cosmic-ray energy equation is described based on the diffusion-convection equation (Drury & Völk 1981; Jones & Kang 1990, Ko 1992), which treats the cosmic rays as a hot massless fluid and neglects the momentum spectrum of cosmic rays to simplify the governing equations. The artificial separation of the cosmic rays from the plasma helps to distinguish the role played by high- and low-energy components.
The cosmic-ray diffusion-convection equation supplements the standard set of ideal MHD equations. The governing equations in the complete vector form are written as
where denotes the plasma fluid velocity; I denotes a unit tensor; denotes the adiabatic index, i.e. ratio of the heat capacity at a constant pressure to that at a constant volume, of the thermal plasma gas; refers to the adiabatic index of the cosmic rays; represents the cosmic-ray diffusivity; represents the rotation angular frequency; and is the external gravitational acceleration. Deriving this equation set involves use of the distribution function in Vlasov equation (Skilling 1975a, b, c). Such governing equations have also been used in the 2D hyperbolic tangent temperature model of Kuwabara, Nakamura & Ko (2004), and the 3D model of Lo, Ko & Wang (2011).
In addition to balancing the energy equations, the term cosmic-ray pressure affects the momentum equation Eq. (2). However, particles of cosmic rays do not interact with plasma directly; they interact with plasma via the magnetic field. On a microscopic scale, resonant scattering of Alfvén waves keeps the cosmic rays nearly isotropically distributed everywhere with respect to the thermal plasma background. A situation in which the cosmic-ray pressure possesses a gradient influences the motion of the plasma gas. Thus, in formulating the equations, the interaction of cosmic-ray particles with a thermal plasma is represented by the cosmic-ray pressure and its gradient. The transport of the cosmic-ray pressure is described by a macroscopic diffusion coefficient, , an energy-weighted mean diffusion tensor, defined as
where denotes a unit vector along the direction.
The limit of this model is mainly that one must assume a priori knowledge of the cosmic-ray pressure and energy density that satisfies the adiabatic index . Here, Eqs. (1)–(5) are solved numerically in a local reference frame in Cartesian coordinates, whose center lies at a galactocentric radius and orbits the galaxy with a fixed angular velocity . In this local frame, the radial, azimuthal, and vertical spatial coordinates are related to the Cartesian coordinates such that , , and . In two dimensions a slice of flow is simulated, and so the rotational effect is not present.
3 Numerical Algorithms
A finite difference method with operator splitting is employed to solve the governing equations. Eqs. (1)–(4) are in the flux-conservative form and solved by 2-Steps Lax-Wendroff explicit method. The cosmic-ray energy equation Eq. (5) is divided into the convection and diffusion parts. The convection part is first converted to a conservative form and then also solved by 2-Steps Lax-Wendroff explicit method. The diffusion part is solved by the Bi-Conjugate Gradients Stabilized (BICGStab) implicit method.
In the 2-step Lax-Wendroff method, Eqs. (1)–(4) and the convection part of Eq. (5) are rewritten in the conservative form:
where can be density , momentums , energy and magnetic field ; ,, are the flux of in -,-,- direction; and is the source term. The component of Eq. (7) is split into two steps:
where superscript denotes time advection and subscript represents space grid.
The diffusion part of Eq. (5) is written as:
whose finite-difference form is expressed as , where the submatrix in and the vector is the function of time step , the cosmic-ray diffusion coefficient , the magnetic field and the cosmic-ray energy at the th iteration. The vector is the unknown:
In order to solve in Eq. (9), the BICGStab method is employed to handle asymmetric linear systems and reduce the operations per iteration to , where is the number of unknowns in the discretized domain. This method is more efficient than the direct solution methods such as decomposition, which require operations. The BICGStab is an iteration method that uses an initial guess to find a corresponding residual , and then iterate to the -th step to an accepted value by means of bi-conjugate matrix-vector operation. For comparison, when solving the nonlinear system with Newton's method:
the correction is determined by solving the gradient of the function, whereas in the BICGStab method,
is used for the iteration. The BICGStab treatment for cosmic-ray energy diffusion equation is an implicit method, and thus the Courant condition is not affected.
4 Normalization and Initial Values
The parameters and variables used in the governing equations withstand an extremely large contrast when expressed in dimensional units, possibly incurring significant errors due to the presence of ill-conditioned matrices and thus infeasible for numerical calculations. To overcome such numerical difficulties, the above equations are normalized to non-dimensional values that are close to unity. The non-dimensional values is denoted by the superscript '*' while the scaling factors are denoted by a '0' subscript. Some of the scaling factors also represent the quantities in equilibrium at the midplane of the Galactic disk.
The length variables are scaled based on the pressure scale height : , , and . is determined by integrating the hydrostatic equilibrium equation:
given the ideal gas law, the values of sound speed , the gravitational acceleration in the -direction, the ratio of plasma pressure to magnetic pressure , the ratio of plasma pressure to cosmic-ray pressure ; and . The gas at the Galactic disk plane is nearly isothermal such that . The sound speed at the disk plane is . Thus, for and , . Given , the velocity is normalized to , and the time scaling factor is defined as , i.e. The ISM density is used to normalize the density, with being about one atom per cubic cm in the ISM, or .
With the above scaling parameters, the mass equation Eq. (1) becomes
which can be converted into . Similarly, the factor at the left hand side of the momentum equation Eq. (2) is balanced by the same factor at the right hand side. The normalized plasma gas pressure is , where , and so the gradient of plasma pressure becomes .
Scaling of the cosmic-ray pressure also employs the gas pressure, . The scaling factor for the magnetic field, , is determined by , and for the Galaxy, .
The gravitational acceleration is scaled to , while the scaling factor for the rotating angular frequency is the reverse of time: . Using the same scaling parameters, the momentum equation Eq. (2), the induction equation Eq. (3) and energy equation Eq. (4) can all be converted to dimensionless values.
Finally, in Eq. (5), the cosmic-ray diffusion coefficient is normalized to , where . Theoretical calculations using path length distribution, life-time of radioactive secondary CR, etc. suggested that the diffusion coefficient for CR above 1 GeV in the Milky Way Galaxy is (Berezinskii et al. 1990; Ptuskin 2001). Due to numerical difficulties with strong magnetic field and large diffusion coefficient, this work adopts a magnetic field strength of several , like those in the solar vicinity, and a times lower than suggested. Crocker et al. (2010) suggest a lower limit of â¼ 50 on 400 pc scales near the Galactic center. However, measurements of the amplitude of the magnetic field depend on the spatial scale and the energy equipartition or pressure equilibrium among various Galactic components, which may differ by 2 orders of magnitude. Pure MHD models with strong magnetic field have been presented in Machida et al. (2009) and Takahashi et al. (2009).
5 Initial Equilibrium Background
We adopt two initial equilibrium backgrounds: a temperature distribution that follows a hyperbolic tangent profile and a density distribution that follows an exponential profile. Both these backgrounds bear a declining density profile with height. They differ mainly in that the hyperbolic tangent temperature has an ascending transition zone that divides the distribution into two distinct regions, while the exponential density follows a continuous decline. Given the temperature or density profile, the profiles for the density/temperature, pressure, magnetic field and other variables can be derived from the hydrostatic condition.
In the isothermal case the criteria for Parker instability to develop is . When the rising field lines grow, the flow becomes unstable. In our cases, the growth of the instability depends on additional parameters such as the width of transition region and the height of Galactic halo (disk thickness).
5.1 Hyperbolic Tangent Temperature
The hyperbolic tangent temperature profile is a two-temperature, layered disk (Shibata et al. 1989a), described by
where is the sound speed, is the disk temperature and is the halo temperature. The initial dimensionless temperature is 1.0, equivalent to . Given the ideal gas law and the gravitational acceleration , the initial density profile is solved using the hydrostatic equation Eq. (10). A constant acceleration is assumed because the grid domain is small and not far way from the disk plane. The dimensionless gravitational acceleration is set as (dimensionless units), equivalent to , or , for . Acceleration can vary widely from galaxy to galaxy. Although a little higher, this value is comparable to the value derived from observations of the spatial density distribution and the velocity-distance correlation pc above the Galactic disk midplane, (Oort 1960; Bahcall 1984; Kuijken & Gilmore 1989). The initial density at the disk plane is (dimensionless units), equivalent to .
After obtaining the density profile, the plasma pressure profile is derived. The magnetic field is assumed to align in the -direction and vary with height , and . The initial dimensionless pressure at the disk is (). The initial magnetic field at the disk for is (dimensionless units), or (), This field strength is very close to the radio synchrotron measurement of 6 averaged over a radius of about 1 kpc around the Sun (Beck 2009).
The initial cosmic-ray pressure at disk for is (dimensionless units), or . The rotating angular frequency (not used in this work) is a free parameter; gives , or approximately times the angular frequency at our Sun, . The initial equilibrium background is assumed quiescent. No initial -velocity and no rotation effects are present in the system.
5.2 Exponential density
The exponential density case produces a nearly isothermal background that is similar to the isothermal model of Kim et al. (1998). However, since imposes singularity in the energy equation, is adopted. The exponential density profile is defined as:
where (dimensionless units), equivalent to ; the density scale (dimensionless units) is equivalent to . The plasma pressure follows . Using Eq. (10), the temperature becomes:
which is a constant. A minimum value of the adiabatic index is adopted in this model. Similar to the hyperbolic tangent model, the initial magnetic field and cosmic-ray pressure are defined through the parameter and , and .
6 Grid Setup and Perturbation
2D simulations are performed in a rectangular domain in the plane. To excite the instability, velocity perturbations are added to the quiescent background. Two perturbation forms are examined: eigenmode sinusoidal wave and random seed. The strong explosive perturbation in CR pressure developed from supernova explosions has been considered in Kuwabara et al. (2004). Notably, although supernova shocks has been believed as efficient cosmic ray accelerator, channeling at least 10% of the supernova explosion energy into cosmic rays, signature of cosmic-ray protons, the key observational evidence in support of the claim that isolated supernova remnants (SNRs) are the main accelerators of galactic CRs, has remained elusive after decades of observational effort (Allen, Houck, & Sturner 2009). Calculations of the maximum energies of shock-accelerated electrons (Reynolds & Keohane 1999) and hydrodynamic simulations of Rayleigh-Taylor instabilities in SNRs (Ferrand et al. 2010, Fraschetti et al. 2010, Wang 2011) both indicate that young SNRs could not be responsible for the highest-energy Galactic cosmic rays, unless an unrealistically high injection rate of cosmic rays, and thus an enormous energy loss in SNRs, is invoked. Precise measurements of cosmic-ray proton and helium spectra by Adriani et al. (2011) furher excludes a single power law energy distribution for the two species and thus challenged the supernova acceleration paradigm.
The sinusoidal perturbation employs a perturbing velocity described by
where is the most unstable wavelength derived from the linear analysis for (Kuwabara et al. 2004). is applied within the region of and , where (dimensionless unit). The grid consists of zones in a rectangular region of . The horizontal length of each grid zone is , while the vertical length is nonuniform:
is increased above by a ratio of 1.05, until . The upper grid domain accommodates the unperturbed magnetic field to avoid outflows across the grid boundary and spurious results.
For the random velocity perturbation (Shore & Larosa 1999), a series of random velocities and with a maximum amplitude of is added horizontally into the background (Chou et al. 2000). The grid covers an area of using zones, with and
7 Results
7.1 Pure MHD Models
We examine how cosmic-ray diffusion affects Parker instability by comparing a series of pure MHD simulations with simulations that include the cosmic-ray effect. Figure 1 illustrates those results using sinusoidal eigenmode perturbations. Figure 1(a) presents the hyperbolic tangent temperature model, while Figure 1(b) displays the exponential density model at the same epoch. In these figures a grid domain of that just lies within the maximum height of the magnetic loops is shown. Logarithmic values of variables in a dimensionless unit are presented in color contours. White solid lines represent the magnetic field lines, and small white arrows refer to the velocity vectors. The superscript '' denoting dimensionless values is omitted hereafter. The exponential model shows a faster growth of the instability because the decline in the gas density facilitates the instability.
7.2 Cosmic-Ray Diffusion Coefficient
Figure 2 compares the maximum height of the magnetic loops versus the cosmic-ray diffusion coefficient in both models at , when the numerical time step becomes very restrained. A smaller CR diffusion coefficient means stronger coupling between the cosmic rays and the plasma. A maximum of ( is examined. In both models, the instability becomes more prominent with an increasing , and the mixing extends to a similarly maximum height of . Because the gradient of cosmic-ray pressure declines with an increasing diffusivity, cosmic-ray diffusion facilitates flow instability. Kuwabara et al. (2004) studied the instability in the hyperbolic tangent temperature case. For small-, the instability is impeded by the CR pressure gradient force that interferes with the falling motion of the matter, while for large-, the magnetic loop can rise to larger scales. Our simulations reach a similar outcome. In Kuwabara et al (2004), the case of strong explosive perturbation in CR pressure presumably from supernova yielded a larger growth rate for a smaller diffusion coefficient, but such a reversed correlation only occurs in the early stage; in the later stage the growth rate becomes smaller when compared to that of a large diffusion coefficient model. In the 3D models of Lo, Ko & Wang (2011) employing sinusoidal perturbations, however, the instability growth first rises with but then drops when , because under strong diffusion, the falling of the gas becomes supersonic; as a result of shock, the cosmic rays are redistributed with a smoother pressure gradient, which tends to stabilize the flow.
7.3 Parameter and
The scale height is set for . Varying modifies the length scale, resulting in different flow structures. Figure 3 presents snapshots of the hyperbolic tangent temperature model with a tenfold gas pressure, ; the flow extends to , which displays more prominent mixing than the case (). Other parameters used are ; ; ; (dimensionless units, or ; ( or ; (); and .
7.4 Parameter and
The temperature distribution is assumed to be uniform in the exponential density model. In this case, modifying and changes only the isothermal temperature value. Notably, the parameter should also influence the scale length (see the scaling for ). However, because cosmic rays largely diffuse along the magnetic field lines, varying does not significantly affect the scale height.
The isothermal case is approximated by using a minimum adiabatic index of . In an ISM, should be significantly smaller than the ideal value and close to , because thermal instability smooths out the temperature gradient. However, because the diffusion of cosmic rays along the magnetic field lines is only slight and the instability growth expedites for more condensed gas, thermal instability is expected to be deterred when cosmic-ray diffusion is present (Shadmehri 2009). This phenomenon may resemble the effect of increasing above the typical value that is used in most of the simulations for Parker instability. According to our results, instability is dampened as increases; with , the flow remains quiescent at (Figure 4a).
In the hyperbolic tangent temperature model, an increasing width of transition region makes the instability less feasible (Figure 4b). Suppression of the instability is attributed to the rapid rise of temperature and the flattening of density near the transition region.
7.5 Random Perturbation
The case using random velocity perturbation may reflect the circumstances closer to the actual situation in an ISM. In this case, the development of instability is slower than the case using eigenmode perturbation, Figure 5 reveals that the exponential density model exhibits slightly higher floatation of the magnetic loops, but similarly strong mixing and filamentary structures are induced in both models.
7.6 Trebly Sinusoidal Perturbation with
The perpendicular or cross field lines diffusion coefficient (see Eq. 6) is often substantially smaller than the parallel coefficient , which is only around of (Ryu et al. 2003). We found that when incorporating cosmic-ray cross field line diffusion , the magnetic field lines are aligned more vertically to the disk. As such a process may be related to the acceleration of galactic wind, a new initial condition using the same equilibrium background is invoked to examine the case involving .
A grid of zones in a domain of is adopted, with each zone having a size identical to the case of random perturbation. The applied velocity perturbation is similar to our previous sinusoidal eigen mode perturbation, but within a finite rectangular region of , where , along with other similar parameters: ; ; ; ; ; ; and .
Figure 6 shows the exponential case at the dimensionless time . Three equally-sized loops arise and extend to . The flow pattern resembles the hyperbolic tangent case in Kuwabara et al. (2004). The interaction between loops becomes more pronounced at later times; the central one becomes compressed by two outer adjacent loops, while the loops continually rise to a height of . At , the flow reaches a maximum vertical height and becomes saturated. Different from the case without , the flow velocity is significantly increased such that the loops rise to a much higher altitude, . Therefore, even at a value of of , the effect of on the mixing appears significant (Figure 6). Although such a result contradicts the estimate made by linear analysis (Ryu et al. 2003), it indicates that Parker instability is likely to contribute to the galactic wind acceleration perpendicular to the galactic disk (Wiegelmann, Schindler, & Neukirch 1997).
8 Conclusion
This study has elucidated the development of Parker instability undergoing cosmic-ray diffusion using 2D MHD simulations. Exactly how the initial conditions affect the growth of instability is examined. Two equilibrium backgrounds are constructed based on hyperbolic tangent temperature and exponential density, with variations in the physical parameters and perturbations.
Our simulations gives rise to a structure that is closely resembles the long, thin wave-like sheared helmet plumes in the solar corona, caused by magnetic buoyancy (Shore & Larosa 1999). The perpendicular component of cosmic-ray diffusion coefficient is included as well. When is only of the parallel component , despite the small development, vertical magnetic structures and outward flow arise, particularly in the exponential density model. The substantial increases in the velocity and altitude of the unstable flow reveal the importance of cosmic rays to the galactic wind. In general, in the exponential density model, the morphology of the clumpy structure is filamentary. Conversely, in the hyperbolic tangent temperature model, a more concentrated and round shape of clumps like the giant molecular cloud are observed at the foot points of rising magnetic arches. The growth of instability in the hyperbolic tangent model is less rapid than that of the exponential density case since the pressure in the exponential density decreases faster with an increasing height.
The small gradient of cosmic ray pressure along the z direction caused by diffusion explains why an increase in facilitates the growth of the unstable undular mode. As a result, the gas falls down more rapidly, and adjacent loops join together to form a large loop-like bubble.
Exponential density with the adiabatic index (i.e. isothermal) produces the highest magnetic loops and most flow instability. A decreasing leads to more condensed gas and, ultimately, a more unstable flow. While examining a situation without cosmic-ray diffusion, Parker indicated that the criterion for instability is . Although the undular mode is expected to be suppressed when , numerical results in our cases using indicate that the high adiabatic index still produces a non-uniform density distribution before the simulations end due to stringent numerical conditions. Therefore, the instability may still occur for large if a stronger perturbation such as a supernova explosion is invoked.
The hyperbolic tangent temperature model yields a density distribution that increases with height, whose steepness depends on the width of the transition zone . For a smaller , instability is increased as the density gradient correspondingly diminishes near the unstable regions.
When a larger ratio of plasma pressure to magnetic pressure is applied, the pressure inside the flux tube diminishes, thus the instability growth is facilitated. Also, as the length scale decreases accordingly, unstable structures are observed on a smaller scale. Contrarily, a small yields a larger scale height and so complicates the mixing of an unstable flow.
Finally, the ratio of plasma pressure to cosmic-ray pressure does not influence the length scale since the diffusion of the cosmic-ray pressure does not contribute to the scale height.
We thank the National Center for High-Performance Computing Center for providing computing facilities and the National Science Council of Taiwan for funding this project under Grants NSC 98-2112-M-033-002, NSC 98-2811-M-033-014 and NSC 98-2811-M-033-020. CMK is supported by the Taiwan National Science Council Grants NSC 98-2923-M-008-01-MY3 and NSC 99-2112-M-008-015-MY3. We are grateful to Jongsoo Kim for helpful comments.
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- Shadmehri M., 2009, MNRAS, 397, 1521
- Skilling J., 1975, MNRAS, 172, 577
- Skilling J., 1975, MNRAS, 173, 245
- Skilling J., 1975, MNRAS, 173, 255
- Tajima T., Shibata K., 1997, Plasma Astrophysics, Reading, Massachusetts: Addison-Wesley
- Takahashi K., Nozawa S., Matsumoto R., Machida M., Fukui Y., Kudo N., Torii K., Yamamoto H., and Fujishita M., 2009, PASJ, 61, 957
- Wang, C.-Y., 2011, MNRAS, 415, 83
- Wiegelmann T., Schindler K., Neukirch T., 1997, Solar Phys., 180, 439
- Zwaan C., 1985, Sol. Phys., 100, 397
- Zwaan C., 1987, ARAA, 25, 83


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Emma Bunton has revealed that she had an "amazing" marriage proposal from her partner Jade Jones last month.
The former Spice Girl explained that she didn't think her boyfriend of 14 years would ever ask her to marry him.
She said on Loose Women: "It was on my birthday and we had friends round, my mum was there and my little boy was on my lap.
"It was absolutely perfect, he couldn't have done it any better. He went down on one knee and picked the ring himself, he did everything! It was just amazing.
"I didn't have a clue! I had been waiting all this time and I thought it was never going to happen."
The 35-year-old, who is expecting her second child with the ex-Damage singer, insisted there was "no pressure" to get married because they've been content for such a long time.
She commented: "With Jade and I, we are such good friends. We have children together, we feel so settled and I just think it felt like the next thing to do. There was no pressure on it.
"I don't get bored but I think you have to get used to [the fact that] there is going to be routine, especially with children. But we make time for date nights and he goes out with the boys, but we love each other's company."
The singer, who is expecting a boy, joked that her baby hasn't stopped moving.
She added: "I can't stop holding my bump at the moment, there is a lot of movement. I am getting kicked all the time! I am due at the end of April, so there is a lot going on in there."


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2019 Kawasaki Ninja ZX-6R Pre-Bookings Open in India, Deliveries to Begin Post January 2019
Customers can pre-book the Kawasaki ZX-6R for an amount of Rs 1.50 lakh and expect delivery of the bike post-January 2019. The pre-booking facility is open from October 31 till November 30, 2018.
2019 Kawasaki Ninja ZX-6R. (Image: Kawasaki)
Kawasaki has announced pre-bookings of the Ninja ZX-6R ABS in India. The supersport Ninja ZX-6R ABS comes with a 636cc in-line liquid cooled four-cylinder engine. The updated Ninja ZX-6R gets updated technological features like KIBS (Kawasaki Intelligent anti-lock Brake System), KTRC (Kawasaki Traction Control), Twin LED headlamps, LED taillight, KQS (Kawasaki Quick Shifter) and a sporty look on the silencer. The Ninja ZX-6R will be assembled locally in India Kawasaki Motor's factory in Chakan, Pune. Customers can pre-book the ZX-6R for an amount of Rs 1.50 lakh and expect delivery of the bike post-January 2019. The pre-booking facility is open from October 31 till November 30, 2018.
Yutaka Yamashita, Managing Director, India Kawasaki Motors said, "First of all we appreciate the support from many Kawasaki fans in India. Our fourth successive championship in Superbike World Championship (also known as WSBK) shows our confidence and expertise in manufacturing supersport bikes in India. ZX-10R is the most affordable championship machine in India. Now by bringing Ninja ZX-6R in India, we are not only expanding the pool of supersport bikes but we are also creating an exciting option in the middleweight class. We are pleased to present an opportunity to supersport enthusiasts as same as ZX-10R. The customers will get an excellent opportunity to pre-book their Ninja ZX-6R during this Diwali."
The clutch technology on the Ninja ZX-6R offers both a back-torque limiting function as well as a light feel at the lever. In addition to this, pressed-aluminium perimeter frame adds to the Ninja ZX-6R's handling, mid-corner composure and an ability to change lines. In terms of looks, the front cowling gets an all-new design. Apart from this, it has also an analogue tachometer flanked by warning lamps on one side, and a gear position indicator and multi-function LCD screen on the other. Bridgestone's sport tyres Battlax Hypersport S22 are utilized on the new motorcycle by Kawasaki.
While the Ninja ZX-6R will be introduced in KRT edition, its ex-showroom price and specifications will be released in due course of time. Like locally assembled Ninja ZX-10R, the Ninja ZX-6R will be available in single seater. As this bike will be produced in limited numbers in first lot, the bookings will be closed after reaching targeted numbers. The future lots of the Ninja ZX-6R will be decided based on the response to the pre-bookings in India.
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Here's a film I did a little work in last year, playing the role of Shona'karakehte. My time was short in this, but I did get in a scene where the rest of the people in the scene were almost … Continue reading
-Today at the FANTASIA INTERNATIONAL FILM FESTIVAL will be the premiere of "Mohawk" (SNOWFORT PICTURES INC). Directed by Ted Geoghegan. This was filmed last year in Upstate NY and I was able to do a couple of days of filming … Continue reading
-Another year has come and gone. I feel like, as I get older, time seems to be moving faster and faster. For many, it seemed like 2016 couldn't end fast enough. IMO, every year has people who do well and … Continue reading
Here's the first look at the film "Mohawk," which just finished principle photography in CNY, from horror magazine RUE MORGUE. This story features interviews with director Ted Geoghegan and actor Jon Huber (AKA Luke Harper from WWE Wrestling). I play … Continue reading
-Last month (June 2016), I got notice of a production that was working in Syracuse-pretty much by a chance meeting. Jeff Meyer told me that the movie "Mohawk" was looking for someone to play a Native American role. While I'm … Continue reading


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Our St Leonards office is looking for an experienced Quality Assurance Administrator with previous administration and document-control experience, to support the Group. This is a newly created role and will require you to bring a mature attitude, initiative and a positive outlook.
Your key responsibilities will include:
You will have:
This position will also require occasional interstate travel.
If you enjoy working in a team and welcome new challenges, this is a great opportunity to grow your career. ACOR is passionate about creating a sustainable company that nurtures its people and provides excellent opportunities for advancement.
How to apply: Please submit a cover letter and your resume
Applicants must have full working rights in Australia and already be residing in the country, to be considered for any role.


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"He passed away today at around 3.30 p.m. His funeral most probably will take place tomorrow at around 11," a source close to Ravi Chopra's family told IANS.
He is survived by his wife and three children.
The 68-year-old "Baghban" director had been reportedly suffering from a severe lung ailment since the last few years.
Son of late B.R. Chopra, Ravi was also known for directing "The Burning Train", "Aaj Ki Awaz", and "Baabul" among others.
RIP Mr Chopra. Thank you for directing such a beautiful and unparalleled version of the Mahabharat. I'm sure you'll be missed by many.
Topic started by Bhavaani
Last replied by RamKiSeeta


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The sneaker community is split pretty drastically around the Legacy 312, and we understand why: The shoes represent a mash-up of some of the most beloved sneakers in the Nike and Jordan archives. Intensely nostalgic sneakerheads have called the combination Don C put together a travesty, but if you're willing to look forward, there's a lot to appreciate about the shoes. Depending on the colorway you grab, the shoes can be bold or subtle, a mirror of how you can see these sneakers as retro inspired or entirely new. There are more colorways of this sneaker coming that haven't released yet so stay tuned.
The first thing you should be looking for when you want to purchase cute sandals is what kinds of materials they are made from. The most common ones are made from leather. This includes not only the straps, but the sole of the sandals as well. The leather is perfect to absorb sweat from your feet as well as endure a lot of wear and tear throughout the hottest months of the year. Leather also stretches as you're wearing it. This means that you're going to be able to have shoes that will mold to your exact shape and size of foot. You will not be locked into the mold that the manufacturer made for the shoe. Instead, you will create the mold using your foot.
Best in class construction- The bedrock of a quality shoe is one that promotes healthy, supported feet. The original BIRKENSTOCK footbed, renowned for expert construction that's been perfected over decades, is the standard of custom comfort. Created with optimal materials to provide overall support and cushioning—cork, jute, plush EVA and suede, among others—our footbed also isolates individual areas to ensure that different regions of the foot are properly served—the toes enjoy extra room for natural movement and foot alignment, and the heel is cradled and cushioned through its deep cup.
Shoes by ASICS. It's what we're known for and it's why you're here. Through technology and design, we bring you performance in the form of footwear that goes unmatched – and we don't even sacrifice style and comfort to do it. Our collection of shoes span various shapes and styles, so that you can be on your A-game, no matter the occasion. Browse the full catalog or get specific with our collections of running shoes, walking shoes, tennis shoes, and training/gym shoes .
What started as a one-off has turned into an ongoing collaboration between Levi's and Jordan brand. The first pair used Levi's blue denim to cover a Jordan 4, creating the first officially sanctioned denim Jordan, years after the Jumpman created some on its own. Golden stitching and Levi's tabs appear all over the sneaker, making for the most authentic translation from dungaree to sportswear possible. Since the first pair, we've seen white and black versions, too. We wouldn't be surprised if the creative partnership continues with new colors materials or on new silhouettes.
Unless you're a hardcore sneaker collector that follows every contour of the sneaker community's ins and outs, you may have missed the second release between Packer Shoes and Adidas on the EQT models. The earlier release on the Cushion 91 set the tone for the partnership, bringing a well-designed sneaker with premium materials into a muddy forest, subverting the idea of streetwear luxury. But the following week, Packer released a pair of the 91/18s in a much more considered design —and in much more limited numbers. The streamlined sneakers pared down the color palate (this time using black, tan, and teal), letting the panels and textures play off one another for a shoe that feels just as engaged with the outdoors but is more progressive in design and sophisticated in palette. A truly quiet winner.
LeBron James put his money where his mouth is for the latest incarnation of his namesake sneaker. Every year he gets the opportunity to start a massive conversation when he releases his latest shoe, and this year he released the very first LeBron 16 with a design by Harlem Fashion Row: a collective of female designers of color lead by Brandice Daniels. Undra Celeste, Kimberly Goldson and Fe Noel. They blended their styles and processes to create a sneaker that works no matter who is wearing it, but delivers a message that breaks barriers not only in opportunities for designers but also in expectations from consumers.
Kendrick Lamar moving from Reebok to Nike was a natural because Nike gave him the Cortez, and nary has a combination of sneaker and artist felt more seamless. Kendrick used the opportunity to put out a series of colorways inspired by his music and evolving identity, offering a range of aesthetics. The Cortez Kenny III is the best one yet. Black, white, and red play off classic sneaker colorways, but Lamar injected the sneakers with details like Chinese characters embroidered into the toe and "BET IT BACK" printed on the tongue ribbon. It's a brilliant pairing.
Sandals are best suited for shorter walks on surfaces that don't have much litter or gravel, which tends to get picked up by any sandal design. Once used to the sandals, some walkers wear them regularly for 10 kilometers or longer walks. While trail sandals are big sellers, hikers often report they are best used for daypacking or in camp rather than when carrying a heavy backpack on natural trails. That said, many long-distance walkers on the Camino de Santiago wear trail sandals some or all of the time. It is an individual choice. You should definitely try them on shorter walks before tackling long distance walks in sandals.


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Pairing and connecting cell phone
Pairing the mobile phone
To avoid becoming distracted and posing an unnecessary hazard both to your own vehicle's occupants and to other road users, only pair the mobile phone while the vehicle is stationary.
1. "Telephone".
2. "Bluetooth® (phone)".
3. "Add new phone".
The Bluetooth name of the vehicle is displayed.
4. To perform additional steps on the mobile phone, refer to the mobile phone operating instructions: e.g. search for or connect the Bluetooth device or a new device.
The Bluetooth name of the vehicle appears on the mobile phone display.
5. Select the Bluetooth name of the vehicle on the mobile phone display.
Prompt via iDrive or the mobile phone to enter the same Bluetooth passkey.
6. Enter the passkey and confirm.
7. Select the functions for which the mobile phone is to be used.
If the pairing was successful, the mobile phone appears at the top of the list of mobile phones.
The functions supported by the mobile phone and audio device are displayed as symbols when paired.
White symbol: the function is active.
Gray symbol: the function is inactive.
Four mobile phones can be paired with the vehicle at once. Three mobile phones can be connected with the vehicle at once.
If pairing was unsuccessful: What to do if...
See also:
Vehicle equipment
All standard, country-specific and optional equipment that is offered in the model series is described in this chapter. Therefore, equipment is also described that is not available in a vehicle, e ...
Switching the microphone to mute
When a call is active, the microphone can be muted. 1. "Telephone" 2. "Active calls" 3. "Microphone mute" A microphone that has been switched to mute is automati ...
BMW X5 xDrive35d: Maintaining the Benchmark with BMW Advanced Diesel
The BMW Advanced Diesel X5 xDrive35d was introduced to the United States as a 2009 model, and despite increased competition remains the fastest, most fuel efficient diesel-powered vehicle in its c ...


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Giveaway: King of Thorns by Mark Lawrence
A few weeks ago I reviewed King of Thorns by Mark Lawrence and gave it a 9/10 (and I also reviewed the first book in the Broken Empire series, Prince of Thorns, and gave it 9/10). Well guess what? …
Post to Tumblr


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Only a person with convictions has a genuine possibility to be tolerant. He who accepts no absolute values but clings to polite doubt cannot be tolerant but merely indifferent. He is morally defenseless in the face of evil.More Erik Kuehnelt-leddihn quotes [03/29/2018 05:03:36]
[T]he democratic principle of "one man, one vote," viewed against a background of voting masses numbering several millions, only serves to demonstrate the pitiful helplessness of the inarticulate individual, who functions at the polls as the smallest indivisible arithmetical (and not always algebraic) unit. He acts in total anonymity, secrecy and legal irresponsibility.More Erik Kuehnelt-leddihn quotes [03/29/2018 05:03:36]
For the average person, all problems date to World War II; for the more informed, to World War I; for the genuine historian, to the French Revolution.More Erik Kuehnelt-leddihn quotes [03/29/2018 05:03:36]
As humanism begins to dominate the state, the consequence is complete hostile annexation of the church or persecution by separation. Religion is then removed from the marketplace and the school, later from other domains of public life. The state will not toerlate any gods besides itself.More Erik Kuehnelt-leddihn quotes [03/29/2018 05:03:36]
Modern man is a hard driven nomad without any stability, not (as the Bible has it) a wanderer or a pilgrim, but a refugee-an escapist. Instead of meditation and reflection there is only speed, fear and "distraction.More Erik Kuehnelt-leddihn quotes [03/29/2018 05:03:36]
Carefree users put like on the shady side of Big Data. [06/13/2019 12:06:20] More
If likes are digital alcohol, many of us are treated late. [06/12/2019 12:06:39] More
The difference between the devil and the angel is that the devil sins constantly, and the angel - sometimes. [05/28/2019 06:05:34] More
Platformization worldly mistakes analog user demand for digital selfish. [06/10/2019 02:06:34] More
Unrequited love is like the dropped anchor of the ship, you want to sail to another person, but it is impossible. [06/13/2019 09:06:23] More


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2015 E Riverside Dr.
Austin TX 78741
The doors open at 6 p.m.
This is a live event. All sales are final. Cancellations and refunds are not accepted.
Section: GA FLOOR, Row: 1
Live Event Admission Ticket
2-hour duration
Section: GA, Row: GA
Section: GENERAL ADMISSION, Row: GA
Mon-Fri: 9am - 5pm CSTSat: 9am - 1pm CST


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Collect or return your rental kit at our Belfast store at no extra cost*
Rental ID: 6546
£3.00 per day
Excluding damage waiver and VAT
A 10% damage waiver fee will be applied to your order in the rental basket unless proof of own insurance can be supplied.
Use the Profoto OCF Snoot to dramatically reduce light spread from off-camera flash, producing a crisp and direct light that's highly efficient, with practically no spill light. It also gives the light a beautifully round shape, which is ideal for use as a hair light or for other applications where only a small portion of an image needs illuminating, such as product or macro photography.
The OCF Snoot is designed to be easy to use – simply snap it onto the front of an off-camera flash and it's ready to shoot. Made from strong glass fiber, it's lightweight and highly durable, making for a useful and hardy addition to any photographer's kit bag along with an off-camera flash unit.
All of our equipment is maintained to the highest standards, with regular servicing, and camera sensors are cleaned before each rental. We have 9 locations across the UK where you can arrange to collect your rental equipment, or we can deliver it to your door. We offer special weekend and weekly rates, and you can open a rental account with Wex to maximise how much you get out of our rental services, including 30-day payment terms and no up-front deposit.
We are dedicated to providing award-winning customer service and competitive pricing to all of our customers. Our rental prices are checked and adjusted weekly to ensure that we remain the most competitively priced photographic rental service within the UK. We also offer a price promise to anyone interested in using our service. If you come across an item from our rental range that is being offered at a cheaper rate by another rental company (including online-only companies), get in touch and we will match their price.


text: Hi there, I have a 6 month old chicken that is limping /not using one of her legs and it is swollen. She has been this way for about a week now. I examined the area and it looked like there might have been a minor lesion in the skin so I have been soaking in epsom salt bath and wrapping. Does anyone have any advice or know what this could be? Thank you very much!


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Click a letter above to view contributors whose names begin with that letter. Click on the name of a contributor to view everything they've shared with LaPorteCountyLife.
Michigan City
5) Michigan City Redevelopment Commission announces expansion of Façade Improvement Program and Upper Story Residential Incentive Program into Midtown area
24) Delta Institute, Michigan City Sanitary District, and Alliance for the Great Lakes Launch Effort to Reduce Pollution from Stormwater in Michigan City with Great Lakes Restoration Initiative Funding
35) Michigan City Announces 2017 Promise Scholarship Recipients: Building a Bright Future for Students and the City
43) Mayor Ron Meer Appoints Former Mayor Chuck Oberlie to the Michigan City Redevelopment Commission


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Husband: Everett Earl Lynds
Born: at: Married: at: Died: at: Father:Frank Lynds Mother:Lillian M. McNutt Other Spouses:
Wife: Peggy Weatherby
Born: at: Died: at: Father: Mother: Other Spouses:
Please use this information as a guide to further your genealogy pursuits.
The information in this database has been provided by
family members from all over the World.
Let me know of any errors, omissions and comments.
Max L. Lynds
P.O. Box 761
Houlton, ME 04730


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All is fair in love and war and, well, pretty much everything else it seems. In fact, do we even know what 'fair' means anymore? By Jamie AdamsRead More
'There is no 'I' in team.' Well, do you know what, I rather think there is.
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The United States Eventing Association (USEA) is excited to continue their partnership with Flair, LLC, maker of FLAIR Equine Nasal Strips. For 2019, Flair, LLC has increased their support of USEA programs by signing on as a Bronze Level sponsor of the USEA Classic Series and Contributing Level sponsor of both the 2019 USEA Intercollegiate Eventing Championships and 2019 USEA American Eventing Championships.
"Flair is proud to be a continuing sponsor of the USEA. The role that USEA plays to build a solid foundation for amateur and professional riders is a key to developing the sport," said Flair CEO and President Jim Chiapetta DVM JD. "This year, we look forward to partnering with USEA, specifically on educational efforts and respiratory health. It's a well-known saying: 'No foot, no horse.' However, the reality is if the horse's lungs aren't working their best, all the feet in the world won't help."
FLAIR Nasal Strips are self-adhesive strips that promote optimum respiratory health of equine athletes at all levels by reducing airway resistance and providing improved airflow when your horse needs oxygen most. Since their introduction at the 1999 Breeder's Cup races and the 2000 Olympics, FLAIR Strips have been regularly used for training and competition by world-class professional horsemen as well as amateur owners around the world. To learn more about their products, visit their website.
"We are extremely thankful to our partners at Flair, LLC for their continued support," said USEA CEO Rob Burk. "We stand by their products and they stand with the sport of eventing. FLAIR Equine Nasal Strips help equine breathe easier, reduce fatigue, conserve energy, and recover faster, all of which is incredibly important for the endurance phase of eventing."
The USEA is a non-profit 501(c)(3) educational organization committed to providing eventing enthusiasts with a competitive level suited to their individual skills. By assisting and educating competitors, event organizers, and officials; maintaining responsible safety standards; and registering qualified competitions and clinics, the USEA offers a strong and continuous training opportunity for an ever-expanding field of world-class competitors. Just as importantly, the USEA provides a means for all riders, regardless of age or ability, to experience the thrill of eventing. To learn more, visit www.useventing.com.
To kick off the Organizers Open Forum at the 2018 USEA Annual Meeting & Convention, Robert Winter provided a report to the organizers in attendance on Xentry and invited organizers to provide feedback on some of the changes that have been implemented.
The United States Eventing Association (USEA) is pleased to announce a new partnership with State Line Tack. As a Bronze Level Sponsor of the 2019 USEA American Eventing Championships (AEC), State Line Tack will award $2,000 worth of prizes for the 22 AEC division winners. This year's AEC will be held August 27-September 1, 2019 at the Kentucky Horse Park in Lexington, Kentucky.
Nestled among the Wasatch Mountain Range in Ogden, Utah lies the Golden Spike Event Center, home of the Golden Spike Horse Trials. For the past 32 years, the Wasatch Pony Club has organized the Golden Spike Horse Trials, welcoming riders from all over the West to experience the beauty of Utah and one of two USEA recognized events in the state.
The USEA Future Event Horse Program (FEH) will host East, West, and Central Championships in September 2019. The West Coast Championships will take place at Twin Rivers Ranch in Paso Robles, California on September 19. The Central Championships will move to Snowdonia Farms in Tomball, Texas the following Thursday, September 26 with the East Coast quickly following Saturday and Sunday, September 28-29 at Loch Moy Farm in Adamstown, Maryland.


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Reiki - Lower Green
Whistley Green is a village in Berkshire, England, and part of the civil parish of St Nicholas Hurst. The settlement lies near to the A321 road, and is located approximately 4.5 miles east of Reading. Wikipedia
Padma Yoga Reiki & Meditation
Arborfield, Berkshire, RG2 9HX
I offer Reiki healing, Reiki shares and Workshops up to Masters Teacher Level ( Over 20 years working with Reiki ) My Story- When I [...]Distance: 11.4 miles.
Healing Energy Solutions
Pangbourne, Berkshire, RG8 7JQ
07811 880595
Relax, destress and re-energise with Reiki healing. Qualified and insured practitioner. Sessions available in Reading, Pangbourne, Tadley, Basingstoke and Wokingham. Homeopathic medicine consultations also available.Distance: 2.3 miles.
Escape and Relax Reiki
Reading, Berkshire, RG8 7JH
Health Benefits of Reiki healing . Promotes health and well-being . Helps with pain management . Encourages mental clarity . Releases stress and tension . Reduces anxiety . Aids relaxation [...]Distance: 2.35 miles.
Theresa Carter Hypnotherapy
Reading, Berkshire, RG30 4QU
07808 218871
A full time qualified Clinical Therapist who can heal the mind and body, with a vast amount of experience within her field.Distance: 4.85 miles.
Lifesource Therapies
Calcot, Berkshire, RG31 7DD
I am a Master Reiki Practitioner and a qualified Holistic and Person Centered Therapist. I have been using Reiki now for many years and am [...]Distance: 5.76 miles.
Gentle Touch Therapies
Reading, Berkshire, RG30
0793 130 1487
Ann runs a successful practice in Reading, Berkshire and offers a range of treatments. Reiki is her most preferred treatment to give and [...]Distance: 6.3 miles.
Rosy Watson. Reiki Energy Healing for People and Animals
Reading, Berkshire, RG4
07786 004383
I am a Reiki Practitioner of the Usui lineage and offer Reiki healing for both people and animals. Together with Reiki I work with other vibrational [...]Distance: 6.43 miles.
The Elbow Room
Wallingford, Oxfordshire, Ox10 0bx
The Elbow Room is a Holistic studio with a variety of treatments , healing and classes . We tailor make each treatment to suit your [...]Distance: 6.85 miles.
Nicky Smith Reiki Master
Reading, Berkshire
Reiki MasterDistance: 7.12 miles.
Pampering Angels
Reading, Berkshire
My name is Jemma, I have over 13 years experience in Reiki and many other specialised treatments. I am very passionate about alternative therapies and [...]Distance: 7.12 miles.
Reading, Berkshire
There are many Reiki Practitioners out there – some qualified and some not. Being a member of the Reiki Guild gives you the assurance [...]Distance: 7.72 miles.
Learn Reiki and Connect
Reading, Berkshire, RG1 3ND
Learn Reiki and Connect offers a range of services tailoring to your needs, whether you are new to Reiki or steadily learning through the courses and [...]Distance: 8.28 miles.
Experience Reiki
Reading, Berkshire, RG7 5UU
077230 46159
My name is Shelley Gore and I offer Reiki Treatments and Reiki attunements level 1,2,3 (Usui Shiki Ryoho) from idylic surroundings in Reading,Berkshire. [...]Distance: 8.4 miles.
GZ Reiki Healer
Reading, Berkshire, RG1 3PA
Hi, My name is Ajmal Khan and I'm a Natural Born Reiki Healer practicing Reiki Healing since 2003. I'm a qualified Psychologist, clinical Counsellor [...]Distance: 8.44 miles.
Wellbeing with Rachel – Yoga teacher & Angelic Reiki Master
Didcot, Oxfordshire, OX11
07958 979455
As a child I always believed in angels, however my enthusiasm was dampened in my teens as I wanted to fit in and talking [...]Distance: 8.85 miles.
Aarion Healing Therapies
Reading, Berkshire, RG7 3XA
Aarion healing is a fully insured and certified practice where you can enjoy either the traditional Usui Reiki energy or the Angelic Reiki energy [...]Distance: 8.98 miles.
Be Good To Yourselves
Three Mile Cross, Berkshire, rg7
I offer my clients a warm peaceful environment and allow unhurried time which helps them to unwind and feel safe enough to release and [...]Distance: 9.25 miles.
Reiki to heal your life
Thatcham, Berkshire, RG19 3RG
01635 866409
Reiki trainer since 2001Distance: 9.3 miles.
Pure Bliss
Oxford, Staffordshire, RG9 2ET
07599 884213
Providing holistic healing through massage, facials and Healthy eating and living. Helping women of all ages to take back control of there health and [...]Distance: 9.33 miles.
Jikiden Reiki with Lisa
Henley-on-Thames, Oxfordshire
JIkiden Reiki- With a warm welcome and relaxing atmopshere come join me in a session of Authentic Japanese Reiki. Whether your looking for relaxing [...]Distance: 9.72 miles.
Jun 2019
Therapy room, Fleet Hampshire
If you have recently trained in Reiki and feel that you need support and maybe want to build your confidence or if you are a practitioner and would like to [...]
Jun 2019
Therapy room, Fleet Hampshire
Have you ever been curious about your past lives? Do you feel you have you lived before? If so, where and when? Who were you? What happened? This workshop* aims [...]
Jul 2019
Therapy room, Fleet Hampshire
In this workshop you will: *Learn about "Ascension" and the new 12 Chakra system * Understand hour four of the Archangels assist in Ascension, connecting with two of them * [...]
Angel card course
Aug 2019
Reading, reading Reading
I use angel cards everyday for either advice or to find out what they would like me to know for that day. It is a lovely way to start communication [...]
Reiki Beginners Course
Sep 2019
Roundwood, Micheldever Hampshire
This is a Reiki Level 1 Course for beginners. Anyone can learn the gentle but powerful healing art of Reiki. Level 4 Reiki Master Teacher, Georgina Watts will guide you in a [...]


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