Local kinetic analysis of low-frequency electrostatic modes in tokamaks

1991 ◽  
Vol 69 (2) ◽  
pp. 102-106
Author(s):  
A. Hirose
Keyword(s):  
Dispersion Relation ◽  
Kinetic Analysis ◽  
Low Frequency ◽  
Acoustic Mode ◽  
Landau Damping ◽  
Trapped Electrons ◽  
Ion Acoustic ◽  
Transit Frequency

Analysis, based on a local kinetic dispersion relation in the tokamak magnetic geometry incorporating the ion transit frequency and trapped electrons, indicates that modes with positive frequencies are predominant. Unstable "drift"-type modes can have frequencies well above the diamagnetic frequency. They have been identified as the destabilized ion acoustic mode suffering little ion Landau damping even when [Formula: see text].

scholarly journals The role of nonlinear Landau damping and the bounced motion of protons in the formation of dissipative structures in the solar wind plasma

1999 ◽  
Vol 6 (3/4) ◽  
pp. 161-167 ◽  
Author(s):  
M. Prakash ◽  
P. H. Diamond
Keyword(s):  
Solar Wind ◽  
Geomagnetic Field ◽  
Large Amplitude ◽  
Solar Wind Plasma ◽  
Acoustic Mode ◽  
Alfven Waves ◽  
Landau Damping ◽  
Alfvén Waves ◽  
Ion Acoustic ◽  
Nonlinear Landau Damping

Abstract. The present work examines the effects arising from the nonlinear Landau damping and the bounced motion of protons (trapped in the mirror geometry of the geomagnetic field) in the formation of nonlinear Alfvénic structures. These structures are observed at distances 1-5AU in the solar wind plasma (with ß ~ 1). The dynamics of formation of these structures can be understood using kinetic nonlinear Schrodinger (KNLS) model. The structures emerge due to balance of nonlinear steepening (of large amplitude Alfvén waves) by the linear Landau damping of ion-acoustic modes in a finite ß solar wind plasma. The ion-acoustic mode is driven nonlinearly by the large amplitude Alfvén waves. At the large amplitudes of Alfvén wave, the effects due to nonlinear Landau damping become important. These nonlinear effects are incorporated into the KNLS model by modifying the heat flux dissipation coefficient parallel to the ambient magnetic field. The effects arising from the bounced motion (of mirroring protons) are studied using a one-dimensional Vlasov equation. The bounced motion of the protons can lead to growth of the ion-acoustic mode, propagating in the mirror geometry of the geomagnetic field. The significance of these studies in the formation of dissipative quasistationary structures observed in solar wind plasma is discussed.

Characteristics of collisional damping of surface ion-acoustic mode in Divertor Plasma Simulator-2 (DiPS-2)

2021 ◽  
Vol 87 (6) ◽  
Author(s):  
Myoung-Jae Lee ◽  
In Sun Park ◽  
Sunghoon Hong ◽  
Kyu-Sun Chung ◽  
Young-Dae Jung
Keyword(s):  
Decay Constant ◽  
Argon Plasma ◽  
Acoustic Mode ◽  
Experimental Simulation ◽  
Landau Damping ◽  
Ion Temperature ◽  
Ion Acoustic ◽  
Collisional Damping ◽  
Weakly Ionized ◽  
The Given

The dissipation of ion-acoustic surface waves propagating in a semi-bounded and collisional plasma which has a boundary with vacuum is theoretically investigated and this result is used for the analysis of edge-relevant plasma simulated by Divertor Plasma Simulator-2 (DiPS-2). The collisional damping of the surface wave is investigated for weakly ionized plasmas by comparing the collisionless Landau damping with the collisional damping as follows: (1) the ratio of ion temperature $({T_i})$ to electron temperature $({T_e})$ should be very small for the weak collisionality $({T_i}/{T_e} \ll 1)$ ; (2) the effect of collisionless Landau damping is dominant for the small parallel wavenumber, and the decay constant is given as $\gamma \approx{-} \sqrt {\mathrm{\pi }/2} {k_\parallel }{\lambda _{De}}\omega _{pi}^2/{\omega _{pe}}$ ; and (3) the collisional damping dominates for the large parallel wavenumber, and the decay constant is given as $\gamma \approx{-} {\nu _{in}}/16$ , where ${\nu _{in}}$ is the ion–neutral collisional frequency. An experimental simulation of the above theoretical prediction has been done in the argon plasma of DiPS-2, which has the following parameters: plasma density ${n_e} = (\textrm{2--9)} \times \textrm{1}{\textrm{0}^{11}}\;\textrm{c}{\textrm{m}^{ - 3}}$ , ${T_e} = 3.7- 3.8\;\textrm{eV}$ , ${T_i} = 0.2- 0.3\;\textrm{eV}$ and collision frequency ${\nu _{in}} = 23- 127\;\textrm{kHz}$ . Although the wavelength should be specified with the given parameters of DiPS-2, the collisional damping is found to be $\gamma = ( - 0.9\;\textrm{to}\; - 5) \times {10^4}\;\textrm{rad}\;{\textrm{s}^{ - 1}}$ for ${k_\parallel }{\lambda _{De}} = 10$ , while the Landau damping is found to be $\gamma = ( - 4\;\textrm{to}\; - 9) \times {10^4}\;\textrm{rad}\;{\textrm{s}^{ - 1}}$ for ${k_\parallel }{\lambda _{De}} = 0.1$ .

Collisional destruction of the Bernstein modes in the high-frequency regime

1976 ◽  
Vol 15 (1) ◽  
pp. 41-48 ◽  
Author(s):  
W. Allan ◽  
J. J. Sanderson
Keyword(s):  
Dispersion Relation ◽  
High Frequency ◽  
Collision Frequency ◽  
Acoustic Mode ◽  
Mode Dispersion ◽  
Ion Acoustic ◽  
Frequency Regime

The paper investigates the effect, on the Bernstein-mode dispersion relation, of a small collision frequency v, such that , for the high-frequency regime. It is shown that the ion-acoustic mode dominates the Bernstein modes in this regime for homogeneous plasmas; and it is suggested that this also holds for inhomogeneous plasmas.

Measurements of the Dispersion Relation of the Low-Frequency Ion Acoustic Instability in the Turbulently Heated TRIAM-1 Tokamak Plasma

1981 ◽  
Vol 20 (1) ◽  
pp. L41-L44
Author(s):  
Osamu Mitarai ◽  
Takechiyo Watanabe ◽  
Yukio Nakamura ◽  
Kazuo Nakamura ◽  
Naoji Hiraki ◽  
...  
Keyword(s):  
Dispersion Relation ◽  
Low Frequency ◽  
Tokamak Plasma ◽  
Acoustic Instability ◽  
Ion Acoustic

Kinetic instability of twisted ion-acoustic mode with superthermal species of plasma

2021 ◽  
Vol 70 ◽  
pp. 196-202
Author(s):  
S. Bukhari ◽  
Syed Raza Ali Raza ◽  
S. Ali
Keyword(s):  
Acoustic Mode ◽  
Ion Acoustic ◽  
Kinetic Instability

scholarly journals Ion Acoustic Peregrine Soliton Under Enhanced Dissipation

2021 ◽  
Vol 8 ◽  
Author(s):  
Pallabi Pathak
Keyword(s):  
Acoustic Wave ◽  
Negative Ions ◽  
Landau Damping ◽  
Ion Acoustic Wave ◽  
Multicomponent Plasma ◽  
Plasma Device ◽  
Ion Acoustic ◽  
Damping Rate ◽  
Double Plasma Device ◽  
Spatial Damping

The effect of enhanced Landau damping on the evolution of ion acoustic Peregrine soliton in multicomponent plasma with negative ions has been investigated. The experiment is performed in a multidipole double plasma device. To enhance the ion Landau damping, the temperature of the ions is increased by applying a continuous sinusoidal signal of frequency close to the ion plasma frequency ∼1 MHz to the separation grid. The spatial damping rate of the ion acoustic wave is measured by interferometry. The damping rate of ion acoustic wave increases with the increase in voltage of the applied signal. At a higher damping rate, the Peregrine soliton ceases to show its characteristics leaving behind a continuous envelope.

Ion-cyclotron modes in weakly relativistic plasmas

1994 ◽  
Vol 51 (3) ◽  
pp. 371-379 ◽  
Author(s):  
Chandu Venugopal ◽  
P. J. Kurian ◽  
G. Renuka
Keyword(s):  
Dispersion Relation ◽  
High Frequency ◽  
Low Frequency ◽  
Dispersion Relations ◽  
The Other ◽  
Larmor Radius ◽  
Relativistic Plasmas ◽  
Ion Plasma ◽  
Maxwellian Plasma ◽  
Relativistic Dispersion

We derive a dispersion relation for the perpendicular propagation of ioncyclotron waves around the ion gyrofrequency ω+ in a weaklu relaticistic anisotropic Maxwellian plasma. These waves, with wavelength greater than the ion Larmor radius rL+ (k⊥ rL+ < 1), propagate in a plasma characterized by large ion plasma frequencies (). Using an ordering parameter ε, we separated out two dispersion relations, one of which is independent of the relativistic terms, while the other depends sensitively on them. The solutions of the former dispersion relation yield two modes: a low-frequency (LF) mode with a frequency ω < ω+ and a high-frequency (HF) mode with ω > ω+. The plasma is stable to the propagation of these modes. The latter dispersion relation yields a new LF mode in addition to the modes supported by the non-relativistic dispersion relation. The two LF modes can coalesce to make the plasma unstable. These results are also verified numerically using a standard root solver.

scholarly journals Kinetic stability properties of relativistic nonneutral electron flow for low-frequency extraordinary-mode perturbations

1989 ◽  
Vol 7 (1) ◽  
pp. 85-109 ◽  
Author(s):  
Ronald C. Davidson ◽  
Han S. Uhm
Keyword(s):  
Dispersion Relation ◽  
Layer Thickness ◽  
Electron Energy ◽  
Electron Flow ◽  
Low Frequency ◽  
Outer Edge ◽  
Stability Properties ◽  
System Parameters ◽  
Wide Range ◽  
Electron Layer

The kinetic stability properties of relativistic nonneutral electron flow in planar diode geometry are examined for extraordinary-mode perturbations about the self-consistent Vlasov equilibrium . Here, the cathode is located at x = 0; the anode is located at x = d the outer edge of the electron layer is located at is the equilibrium flow velocity in the x-direction; n^b is the electron density at the cathode (x = 0); and is the axial magnetic field, with const. in the vacuum region (xb < x ≤ d). The extraordinary-mode eigenvalue equation, derived in a companion paper for low-frequency, long-wavelength perturbations, is solved exactly. This leads to a formal dispersion relation, which can be used to determine the complex eigenfrequency ω over a wide range of system parameters and wavenumber k in the y-direction. The formal dispersion relation is further simplified for and , assuming low-frequency perturbations about a tenuous electron layer with and . Here, , and , where denotes the average equilibrium orbit, and [γ(x) − 1]mc2 is the average kinematic energy of an electron fluid element. The resulting approximate dispersion relation is solved numerically over a wide range of system parameters to determine the detailed dependence of stability properties on electromagnetic effects, layer thickness, and electron energy, as measured by , and γb − 1, respectively. Here, γb = γ(xb) denotes the electron energy at the outer edge of the electron layer. As a general remark, it is found that increasing the electron energy (γb − 1), increasing the strength of electromagnetic effects , and/or decreasing the layer thickness (xb/d) all have a stabilizing influence.

scholarly journals An introductory guide to fluid models with anisotropic temperatures. Part 2. Kinetic theory, Padé approximants and Landau fluid closures

2019 ◽  
Vol 85 (6) ◽  
Author(s):  
P. Hunana ◽  
A. Tenerani ◽  
G. P. Zank ◽  
M. L. Goldstein ◽  
G. M. Webb ◽  
...  
Keyword(s):  
Kinetic Theory ◽  
Fourth Order ◽  
Low Frequency ◽  
Padé Approximants ◽  
Landau Damping ◽  
Order Moment ◽  
Fluid Models ◽  
Frequency Limit ◽  
Long Wavelength ◽  
Pade Approximants

In Part 2 of our guide to collisionless fluid models, we concentrate on Landau fluid closures. These closures were pioneered by Hammett and Perkins and allow for the rigorous incorporation of collisionless Landau damping into a fluid framework. It is Landau damping that sharply separates traditional fluid models and collisionless kinetic theory, and is the main reason why the usual fluid models do not converge to the kinetic description, even in the long-wavelength low-frequency limit. We start with a brief introduction to kinetic theory, where we discuss in detail the plasma dispersion function $Z(\unicode[STIX]{x1D701})$ , and the associated plasma response function $R(\unicode[STIX]{x1D701})=1+\unicode[STIX]{x1D701}Z(\unicode[STIX]{x1D701})=-Z^{\prime }(\unicode[STIX]{x1D701})/2$ . We then consider a one-dimensional (1-D) (electrostatic) geometry and make a significant effort to map all possible Landau fluid closures that can be constructed at the fourth-order moment level. These closures for parallel moments have general validity from the largest astrophysical scales down to the Debye length, and we verify their validity by considering examples of the (proton and electron) Landau damping of the ion-acoustic mode, and the electron Landau damping of the Langmuir mode. We proceed by considering 1-D closures at higher-order moments than the fourth order, and as was concluded in Part 1, this is not possible without Landau fluid closures. We show that it is possible to reproduce linear Landau damping in the fluid framework to any desired precision, thus showing the convergence of the fluid and collisionless kinetic descriptions. We then consider a 3-D (electromagnetic) geometry in the gyrotropic (long-wavelength low-frequency) limit and map all closures that are available at the fourth-order moment level. In appendix A, we provide comprehensive tables with Padé approximants of $R(\unicode[STIX]{x1D701})$ up to the eighth-pole order, with many given in an analytic form.

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