scholarly journals Particle trajectories in Weibel filaments: influence of external field obliquity and chaos

2020 ◽  
Vol 86 (3) ◽  
Author(s):  
A. Bret ◽  
M. E. Dieckmann
Keyword(s):  
External Field ◽  
Collisionless Plasma ◽  
Plasma Phys ◽  
Incoming Flow ◽  
Particle Trajectories ◽  
Order Unity ◽  
Incoming Particle ◽  
Test Particles ◽  
Overlapping Region ◽  
Peak Value

When two collisionless plasma shells collide, they interpenetrate and the overlapping region may turn Weibel unstable for some values of the collision parameters. This instability grows magnetic filaments which, at saturation, have to block the incoming flow if a Weibel shock is to form. In a recent paper (Bret, J. Plasma Phys., vol. 82, 2016b, 905820403), it was found by implementing a toy model for the incoming particle trajectories in the filaments, that a strong enough external magnetic field $\unicode[STIX]{x1D63D}_{0}$ can prevent the filaments blocking the flow if it is aligned with them. Denoting by $B_{f}$ the peak value of the field in the magnetic filaments, all test particles stream through them if $\unicode[STIX]{x1D6FC}=B_{0}/B_{f}>1/2$ . Here, this result is extended to the case of an oblique external field $B_{0}$ making an angle $\unicode[STIX]{x1D703}$ with the flow. The result, numerically found, is simply $\unicode[STIX]{x1D6FC}>\unicode[STIX]{x1D705}(\unicode[STIX]{x1D703})/\cos \unicode[STIX]{x1D703}$ , where $\unicode[STIX]{x1D705}(\unicode[STIX]{x1D703})$ is of order unity. Noteworthily, test particles exhibit chaotic trajectories.

scholarly journals Particle trajectories in Weibel magnetic filaments with a flow-aligned magnetic field

2016 ◽  
Vol 82 (4) ◽  
Author(s):  
Antoine Bret
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Initial Velocity ◽  
Larmor Radius ◽  
Shock Formation ◽  
Incoming Flow ◽  
Particle Trajectories ◽  
Overlapping Region ◽  
Peak Field ◽  
Aligned Magnetic Field

For a Weibel shock to form, two plasma shells have to collide and trigger the Weibel instability. At saturation, this instability generates magnetic filaments in the overlapping region with peak field $B_{f}$. In the absence of an external guiding magnetic field, these filaments can block the incoming flow, initiating the shock formation, if their size is larger than the Larmor radius of the incoming particles in the peak field. Here we show that this result still holds in the presence of an external magnetic field $B_{0}$, provided it is not too high. Yet, for $B_{0}\gtrsim B_{f}/2$, the filaments become unable to stop any particle, regardless of its initial velocity.

scholarly journals Reduced models accounting for parallel magnetic perturbations: gyrofluid and finite Larmor radius–Landau fluid approaches

2016 ◽  
Vol 82 (6) ◽  
Author(s):  
E. Tassi ◽  
P. L. Sulem ◽  
T. Passot
Keyword(s):  
Fluid Model ◽  
Collisionless Plasma ◽  
Low Frequency ◽  
Wave Model ◽  
Plasma Phys ◽  
Alfven Wave ◽  
Larmor Radius ◽  
Closure Relation ◽  
Reduced Models ◽  
Finite Larmor Radius

Reduced models are derived for a strongly magnetized collisionless plasma at scales which are large relative to the electron thermal gyroradius and in two asymptotic regimes. One corresponds to cold ions and the other to far sub-ion scales. By including the electron pressure dynamics, these models improve the Hall reduced magnetohydrodynamics (MHD) and the kinetic Alfvén wave model of Boldyrev et al. (2013 Astrophys. J., vol. 777, 2013, p. 41), respectively. We show that the two models can be obtained either within the gyrofluid formalism of Brizard (Phys. Fluids, vol. 4, 1992, pp. 1213–1228) or as suitable weakly nonlinear limits of the finite Larmor radius (FLR)–Landau fluid model of Sulem and Passot (J. Plasma Phys., vol 81, 2015, 325810103) which extends anisotropic Hall MHD by retaining low-frequency kinetic effects. It is noticeable that, at the far sub-ion scales, the simplifications originating from the gyroaveraging operators in the gyrofluid formalism and leading to subdominant ion velocity and temperature fluctuations, correspond, at the level of the FLR–Landau fluid, to cancellation between hydrodynamic contributions and ion finite Larmor radius corrections. Energy conservation properties of the models are discussed and an explicit example of a closure relation leading to a model with a Hamiltonian structure is provided.

Low-frequency waves in a high-beta collisionless plasma: polarization, compressibility and helicity

1986 ◽  
Vol 35 (3) ◽  
pp. 431-447 ◽  
Author(s):  
S. Peter Gary
Keyword(s):  
Numerical Solutions ◽  
Collisionless Plasma ◽  
Low Frequency ◽  
Order Unity ◽  
Left Hand ◽  
Long Wavelength ◽  
Oblique Propagation ◽  
Ion Cyclotron ◽  
Cyclotron Mode ◽  
High Beta

This paper considers the linear theory of waves near and below the ion cyclotron frequency in an isothermal electron-ion Vlasov plasma which is isotropic, homogeneous and magnetized. Numerical solutions of the full dispersion equation for the magnetosonic/whistler and Alfvén/ion cyclotron modes at βi = 1·0 are presented, and the polarizations, compressibilities, helicities, ion Alfvén ratios and ion cross-helicities are exhibited and compared. At sufficiently large βi and θ, the angle of propagation with respect to the magnetic field, the real part of the polarization of the Alfvén/ion cyclotron wave changes sign, so that, for such parameters, this mode is no longer left-hand polarized. The Alfvén/ion cyclotron mode becomes more compressive as the wavenumber ulereases, whereas the magnetosonic/whistler becomes more compressive with increasing θ, At oblique propagation, the helicity of both modes approaches zero in the long-wavelength limit; in contrast, the ion cross-helicity is of order unity for the Alfvén/ion cyclotron wave and decreases as θ increases for the magnetosonic/whistler mode.

Relativistic collisionless shocks formation in pair plasmas

2013 ◽  
Vol 79 (4) ◽  
pp. 367-370 ◽  
Author(s):  
ANTOINE BRET ◽  
A. STOCKEM ◽  
F. FIUZA ◽  
C. RUYER ◽  
L. GREMILLET ◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Reasonable Agreement ◽  
Collisionless Plasma ◽  
The Other ◽  
Shock Formation ◽  
Linear Phase ◽  
Collisionless Shocks ◽  
Seed Field ◽  
The One ◽  
Overlapping Region

AbstractCollisionless shocks are ubiquitous in astrophysics and in the laboratory. Recent numerical simulations and experiments have shown how these can arise from the encounter of two collisionless plasma shells. When the shells interpenetrate, the overlapping region turns unstable, triggering the shock formation. As a first step toward a microscopic understanding of the process, we here analyze in detail the initial instability phase. On the one hand, 2D relativistic PIC simulations are performed where two unmagnetized, symmetric, and initially cold pair plasmas collide. On the other hand, the instabilities at work are analyzed, as well as the field at saturation and the seed field which gets amplified. For mildly relativistic motions and onward, Weibel modes with ω=0+iδ govern the linear phase. We derive an expression for the duration of the linear phase in reasonable agreement with the simulations.

scholarly journals Theory of the formation of a collisionless Weibel shock: pair vs. electron/proton plasmas

2016 ◽  
Vol 34 (2) ◽  
pp. 362-367 ◽  
Author(s):  
A. Bret ◽  
A. Stockem Novo ◽  
R. Narayan ◽  
C. Ruyer ◽  
M. E. Dieckmann ◽  
...  
Keyword(s):  
Mean Free Path ◽  
Particle Accelerators ◽  
Incoming Flow ◽  
Collisionless Shock ◽  
Collisionless Shocks ◽  
Trapping Time ◽  
Particle In Cell ◽  
The Mean ◽  
The One ◽  
Overlapping Region

AbstractCollisionless shocks are shocks in which the mean-free path is much larger than the shock front. They are ubiquitous in astrophysics and the object of much current attention as they are known to be excellent particle accelerators that could be the key to the cosmic rays enigma. While the scenario leading to the formation of a fluid shock is well known, less is known about the formation of a collisionless shock. We present theoretical and numerical results on the formation of such shocks when two relativistic and symmetric plasma shells (pair or electron/proton) collide. As the two shells start to interpenetrate, the overlapping region turns Weibel unstable. A key concept is the one of trapping time τp, which is the time when the turbulence in the central region has grown enough to trap the incoming flow. For the pair case, this time is simply the saturation time of the Weibel instability. For the electron/proton case, the filaments resulting from the growth of the electronic and protonic Weibel instabilities, need to grow further for the trapping time to be reached. In either case, the shock formation time is 2τp in two-dimensional (2D), and 3τp in 3D. Our results are successfully checked by particle-in-cell simulations and may help designing experiments aiming at producing such shocks in the laboratory.

scholarly journals Plasma sheath and presheath development near a partially reflective surface

2021 ◽  
Vol 87 (1) ◽  
Author(s):  
Boris N. Breizman ◽  
Dmitrii I. Kiramov
Keyword(s):  
Rarefaction Wave ◽  
Collisionless Plasma ◽  
Plasma Phys ◽  
Plasma Sheath ◽  
One Dimensional ◽  
Flow Parameters ◽  
Wall Potential ◽  
Electron Reflection ◽  
Strong Reflection ◽  
Self Similar

This work addresses one-dimensional evolution of a collisionless plasma next to a solid surface that is immersed into the plasma instantaneously. In particular, we consider how the self-similar rarefaction wave (Allen & Andrews, J. Plasma Phys., vol. 4, 1970, pp. 187–194) establishes dynamically and how the electron reflection from the surface modifies the structure of the rarefaction wave and the Debye sheath. We demonstrate that a sufficiently strong reflection eliminates the Debye sheath and changes the wall potential and the plasma flow parameters significantly. The paper presents numerical results that illustrate the developed analytical theory.

scholarly journals Motion of particles and gravitational lensing around the (2+1)-dimensional BTZ black hole in Gauss–Bonnet gravity

2021 ◽  
Vol 81 (9) ◽  
Author(s):  
Bakhtiyor Narzilloev ◽  
Sanjar Shaymatov ◽  
Ibrar Hussain ◽  
Ahmadjon Abdujabbarov ◽  
Bobomurat Ahmedov ◽  
...  
Keyword(s):  
Black Hole ◽  
Gravitational Lensing ◽  
Coupling Constant ◽  
Btz Black Hole ◽  
Bending Angle ◽  
Four Dimensions ◽  
Approach Distance ◽  
Test Particles ◽  
The One ◽  
Peak Value

AbstractWe study the motion of test particles and photons in the vicinity of the (2+1)-dimensional Gauss–Bonnet (GB) BTZ black hole. We find that the presence of the coupling constant serves as an attractive gravitational charge, shifting the innermost stable circular orbits outward with respect to the one for this theory in four dimensions. Further, we consider the gravitational lensing, to test the GB gravity in (2+1) dimensions and show that the presence of the GB parameter causes the bending angle to first increase with the increase in the inverse of the closest approach distance, $$u_0$$ u 0 , reaching a peak value for a specific $$u_0^*$$ u 0 ∗ , and then decreasing to zero. We also show that the increase in the value of the GB parameter decreases the bending angle, and the increase in the absolute value of the negative cosmological constant produces an opposite effect on this angle.

A novel analytical calculation of magnetic field in the slotted air gap of spoke-type permanent-magnet machines using conformal mapping

2020 ◽  
pp. 1-15
Author(s):  
Jianqi Li ◽  
Yu Zhou ◽  
Jianying Li
Keyword(s):  
Magnetic Field ◽  
Conformal Mapping ◽  
Permanent Magnet ◽  
Flux Density ◽  
Analytical Method ◽  
Electromotive Force ◽  
Analytical Calculation ◽  
Air Gap ◽  
Permanent Magnet Machines ◽  
Peak Value

This paper presented a novel analytical method for calculating magnetic field in the slotted air gap of spoke-type permanent-magnet machines using conformal mapping. Firstly, flux density without slots and complex relative air-gap permeance of slotted air gap are derived from conformal transformation separately. Secondly, they are combined in order to obtain normalized flux density taking account into the slots effect. The finite element (FE) results confirmed the validity of the analytical method for predicting magnetic field and back electromotive force (BEMF) in the slotted air gap of spoke-type permanent-magnet machines. In comparison with FE result, the analytical solution yields higher peak value of cogging torque.

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