A comparative study of the filamentation and Weibel instabilities and their cumulative effect. I. Non-relativistic theory

2009 ◽  
Vol 75 (1) ◽  
pp. 19-33 ◽  
Author(s):  
M. LAZAR ◽  
A. SMOLYAKOV ◽  
R. SCHLICKEISER ◽  
P. K. SHUKLA
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Distribution Function ◽  
Comparative Study ◽  
Relativistic Theory ◽  
Thermal Emission ◽  
Cumulative Effect ◽  
Fusion Plasma ◽  
Thermal Anisotropy ◽  
Maxwellian Distribution Function

AbstractA comparative study of the electromagnetic instabilities in anisotropic unmagnetized plasmas is undertaken. The instabilities considered are the filamentation and Weibel instability, and their cumulative effect. Dispersion relations are derived and the growth rates are plotted systematically for the representative cases of non-relativistic counterstreaming plasmas with isotropic or anisotropic velocity distributions functions of Maxwellian type. The pure filamentation mode is attenuated by including an isotropic Maxwellian distribution function. Moreover, it is observed that counterstreaming plasmas can be fully stabilized by including bi-Maxellian distributions with a negative thermal anisotropy. This effect is relevant for fusion plasma experiments. Otherwise, for plasma streams with a positive anisotropy the filamentation and Weibel instabilities cumulate leading to a growth rate by orders of magnitude larger than that of a simple filamentation mode. This is noticeable for the quasistatic magnetic field generated in astrophysical sources, and which is expected to saturate at higher values and explain the non-thermal emission observed.

Cyclotron instabilities of a magnetized electron plasma with anisotropic temperatures

1977 ◽  
Vol 17 (3) ◽  
pp. 453-465 ◽  
Author(s):  
C. Chiuderi ◽  
G. Einaudi ◽  
R. Giachetti
Keyword(s):  
Magnetic Field ◽  
Distribution Function ◽  
Dispersion Relation ◽  
Growth Rates ◽  
Linear Growth ◽  
Electron Plasma ◽  
Maxwellian Distribution ◽  
Analytical Treatment ◽  
Maxwellian Distribution Function ◽  
Instability Regions

The dispersion relation for an electron plasma in a magnetic field is investigated for a bi-Maxwellian distribution function. A new set of solutions for non-perpendicular propagation is found. The linear growth rates are computed and the instability regions in the (k, cos θ) plane are determined. An approximate analytical treatment of the problem is also given for certain ranges of the parameters.

Effect of electron thermal anisotropy on the kinetic cross-field streaming instability

1984 ◽  
Vol 32 (1) ◽  
pp. 159-178 ◽  
Author(s):  
S. T. Tsai ◽  
M. Tanaka ◽  
J. D. Gaffey ◽  
E. H. Da Jornada ◽  
C. S. Wu ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Shock Waves ◽  
Numerical Solutions ◽  
Collisionless Shock ◽  
Direction Transverse ◽  
Ambient Magnetic Field ◽  
Thermal Anisotropy ◽  
Analytical And Numerical Solutions ◽  
Streaming Instability

The investigation of the kinetic cross-field streaming instability, motivated by the research of collisionless shock waves and previously studied by Wu et al., is discussed more fully in the present work. Since, in the ramp region of a quasi-perpendicular shock, electrons can be preferentially heated in the direction transverse to the ambient magnetic field, it is both desirable and necessary to include the effect of the thermal anisotropy on the instability associated with a shock. The present study has found that Te⊥ > Te‖ can significantly enhance the peak growth rate of the cross-field streaming instability when the electron beta is sufficiently high. Furthermore, the present analysis also improves the analytical and numerical solutions previously obtained.

Particle losses due to RF-enhanced pitch-angle scattering into velocity space loss regions

1984 ◽  
Vol 32 (2) ◽  
pp. 273-281 ◽  
Author(s):  
D. Anderson ◽  
M. Lisak
Keyword(s):  
Magnetic Field ◽  
Distribution Function ◽  
Pitch Angle ◽  
High Energy ◽  
Velocity Space ◽  
Rf Heating ◽  
Fusion Plasma ◽  
Angle Scattering ◽  
Heated Particle ◽  
Scattering Losses

The application of RF heating (ICRH or LHH) to a fusion plasma creates high-energy tails on the distribution function of the heated particle species. In the presence of loss regions in velocity space, e. g. due to particle drifts in the toroidal magnetic field ripple of a tokamak, the collisional pitch-angle scattering losses may be significantly enhanced. The present work assesses the importance of such RF-enhanced losses and explicit expressions are derived for the evolution of the loss fraction. In particular, for parameters typical of PLT we find that the loss fraction could rapidly reach high values.

scholarly journals Beam effect on electromagnetic ion-cyclotron waves with general loss – cone distribution function in an anisotropic plasma-particle aspect analysis

2007 ◽  
Vol 25 (2) ◽  
pp. 557-568 ◽  
Author(s):  
G. Ahirwar ◽  
P. Varma ◽  
M. S. Tiwari
Keyword(s):  
Growth Rate ◽  
Distribution Function ◽  
Ion Beam ◽  
Temperature Anisotropy ◽  
Loss Cone ◽  
Thermal Anisotropy ◽  
Ion Cyclotron ◽  
Electromagnetic Ion Cyclotron Waves ◽  
The Waves ◽  
Emic Waves

Abstract. The effect of upgoing ion beam and temperature anisotropy on the dispersion relation, growth rate, parallel and perpendicular resonant energies, and marginal instability of the electromagnetic ion cyclotron (EMIC) waves, with general loss-cone distribution function, in a low β homogeneous plasma, is discussed by investigating the trajectories of the charged particles. The whole plasma is considered to consist of resonant and non-resonant particles. The resonant particles participate in an energy exchange with the waves, whereas the non-resonant particles support the oscillatory motion of the waves. The effects of the steepness of the loss-cone distribution, ion beam velocity, with thermal anisotropy on resonant energy transferred, and the growth rate of the EMIC waves are discussed. It is found that the effect of the upgoing ion beam is to reduce the energy of transversely heated ions, whereas the thermal anisotropy acts as a source of free energy for the EMIC waves and enhances the growth rate. It is found that the EMIC wave emissions occur by extracting energy of perpendicularly heated ions in the presence of an upflowing ion beam and a steep loss-cone distribution function in the anisotropic magnetoplasma. The effect of the steepness of the loss-cone is also to enhance the growth rate of the EMIC waves. The results are interpreted for EMIC emissions in the auroral acceleration region.

Ripple modifications to alpha transport in tokamaks

2018 ◽  
Vol 84 (5) ◽  
Author(s):  
Peter J. Catto
Keyword(s):  
Magnetic Field ◽  
Distribution Function ◽  
Power Plants ◽  
Collision Operator ◽  
Radial Transport ◽  
Flux Surface ◽  
Slowing Down ◽  
Transport Losses ◽  
Maxwellian Distribution Function ◽  
Major Radius

Magnetic field ripple is inherent in tokamaks since the toroidal magnetic field is generated by a finite number of toroidal field coils. The field ripple results in departures from axisymmetry that cause radial transport losses of particles and heat. These ripple losses are a serious concern for alphas near their birth speed $v_{0}$ since alpha heating of the background plasma is required to make fusion reactors into economical power plants. Ripple in tokamaks gives rise to at least two alpha transport regimes of concern. As the slowing down time $\unicode[STIX]{x1D70F}_{s}$ is much larger than the time for an alpha just born to make a toroidal transit, a regime referred to as the $1/\unicode[STIX]{x1D708}\propto \unicode[STIX]{x1D70F}_{s}$ regime can be encountered, with $\unicode[STIX]{x1D708}$ the appropriate alpha collision frequency. In this regime the radial transport losses increase as $v_{0}\unicode[STIX]{x1D70F}_{s}/R$, with $R$ the major radius of the tokamak. The deleterious effect of ripple transport is mitigated by electric and magnetic drifts within the flux surface. When drift tangent to the flux surface becomes significant another ripple regime, referred to as the $\sqrt{\unicode[STIX]{x1D708}}$ regime, is encountered where a collisional boundary layer due to the drift plays a key role. We evaluate the alpha transport in both regimes, taking account of the alphas having a slowing down rather than a Maxwellian distribution function and their being collisionally scattered by a collision operator appropriate for alphas. Alpha ripple transport is found to be in the $\sqrt{\unicode[STIX]{x1D708}}$ regime where it will be a serious issue for typical tokamak reactors as it will be well above the axisymmetric neoclassical level and can be large enough to deplete the alpha slowing down distribution function unless toroidal rotation is strong.

The L mode in electromagnetic proton-cyclotron waves in plasmas modelled by a Lorentzian distribution function

1998 ◽  
Vol 60 (1) ◽  
pp. 29-48 ◽  
Author(s):  
PEDRO VEGA ◽  
LUIS PALMA ◽  
RENE ELGUETA
Keyword(s):  
Magnetic Field ◽  
Distribution Function ◽  
Growth Rates ◽  
Maximum Growth ◽  
High Energy ◽  
Thermal Anisotropy ◽  
Proton Concentration ◽  
Lorentzian Distribution ◽  
High Energy Tail ◽  
Proton Cyclotron

The L mode in electromagnetic proton-cyclotron waves (EPCWs) propagating parallel to a uniform ambient magnetic field is studied here analytically. A generalized Lorentzian distribution function is used to model the plasma. Analytical expressions for the wavenumber and for both the temporal and convective growth rates for a multi-ion plasma are obtained within the linear theory. This analytical approach is appropiate for β∥<1, which is the ratio of plasma kinetic pressure to magnetic field pressure. The characteristics of the unstable spectrum are found to be independent of high-energy particles. For a plasma composed of electrons plus hot and cold protons, it is shown that the maximum growth rates as functions of cold-proton concentration δ can always decrease, or can increase until δ reaches a certain peak value and decrease thereafter, or can always increase, depending on the thermal anisotropy of the hot protons. This behaviour is similar to that in Maxwellian plasmas. However, for the convective growth rate, the expression for the optimum cold-proton concentration shows a significant dependence on the spectral index κ. Therefore, when cold protons are injected, it is more difficult to obtain optimum amplification in a Lorentzian plasma than in a Maxwellian plasma. It is also shown that the influence of the high-energy tail on the generation and amplification processes of the EPCWs is controlled by thermal anisotropy and cold-ion population. As a consequence of the latter, temporal and convective growth rates can be larger than, equal to or smaller than those of Maxwellian plasmas, depending on the anisotropy of the hot-proton distribution and on the cold-proton concentration.

A comparative study of the filamentation and Weibel instabilities and their cumulative effect. II. Weakly relativistic beams

2009 ◽  
Vol 75 (4) ◽  
pp. 529-543 ◽  
Author(s):  
A. STOCKEM ◽  
M. LAZAR ◽  
P. K. SHUKLA ◽  
A. SMOLYAKOV
Keyword(s):  
Comparative Study ◽  
Gamma Ray ◽  
Numerical Solutions ◽  
Cumulative Effect ◽  
Plasma Phys ◽  
Large Temperature ◽  
Temperature Anisotropy ◽  
Fusion Plasma ◽  
Gamma Ray Burst ◽  
Transverse Temperature

AbstractCounterstreaming plasma systems with intrinsic temperature anisotropies are unstable against the excitation of Weibel-type instabilities, namely, filamentation and Weibel instabilities, and their cumulative effect. Here, the analysis is extended to counterstreaming plasmas with weakly relativistic bulk velocities, while the thermal velocities are still considered to be non-relativistic. Such plasma systems are relevant for fusion plasma experiments and the more violent astrophysical phenomena, such as jets in gamma-ray burst sources. Simple analytical forms of the dispersion relations are derived in the limit of a small transverse temperature or a large temperature anisotropy of the beams. The aperiodic growing solutions are plotted systematically for the representative cases chosen in Paper I (Lazar et al. 2009 J. Plasma Phys. 75, in press). In the limit of slow non-relativistic plasma flows, the numerical solutions fit well with those obtained in Paper I, but for weakly relativistic streams an important deviation is found.

scholarly journals Effect of ion beam on electromagnetic ion cyclotron instability in hot anisotropic plasma-particle aspect analysis

2011 ◽  
Vol 29 (8) ◽  
pp. 1469-1478 ◽  
Author(s):  
S. Patel ◽  
P. Varma ◽  
M. S. Tiwari ◽  
N. Shukla
Keyword(s):  
Growth Rate ◽  
Distribution Function ◽  
Ion Beam ◽  
Anisotropic Plasma ◽  
Loss Cone ◽  
Thermal Anisotropy ◽  
Beam Velocity ◽  
Emic Wave ◽  
Ion Cyclotron ◽  
Particle Aspect Analysis

Abstract. Using the general loss-cone distribution function electromagnetic ion cyclotron (EMIC) instability affected by up going ion beam has been studied by investigating the trajectories of charged particles. The plasma consisting of resonant and non-resonant particles has been considered. It is assumed that the resonant particles participate in energy exchange with the wave, whereas non-resonant particles support the oscillatory motion of the wave. The effect of ion beam velocity on the dispersion relation, growth rate, parallel and perpendicular resonant energy of the EMIC wave with general loss-cone distribution function in hot anisotropic plasma is described by particle aspect approach. The effect of beam anisotropy and beam density on electromagnetic ion cyclotron instabilities is investigated. Growth length is derived for EMIC waves in hot anisotropic plasma. It is found that the effect of the ion beam is to reduce the energy of transversely heated ions, whereas the thermal anisotropy of the background plasma acts as a source of free energy for the EMIC wave and enhances the growth rate. It is observed that ion beam velocity opposite to the wave propagation and its density reduces the growth rate and enhance the reduction in perpendicularly heated ions energy. The effect of ion beam anisotropy on EMIC wave is also discussed. These results are determined for auroral acceleration region. It is also found that the EMIC wave emissions occur by extracting energy of perpendicularly heated ions in the presence of an up flowing ion beam.

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