Mercier--Cotsaftis and Grad--Shafranov equations for anisotropic plasma
In this brief review, the historical aspects of the generalization of the Grad--Shafranov equation to the case of anisotropic plasma are discussed.
physics.plasm-ph↗
arXiv subjects
Igor Kotelnikov
Publications and source records attributed to Igor Kotelnikov.
Theory of a dynamic plasma flow pressure sensor
The problem of reconstructing the time dependence of the dynamic pressure of a plasma jet impinging on one end of a solid rod based on the measured displacement of the opposite end has been solved. This solution allows for a reduction in the size of the dynamic pressure sensor proposed and later improved in the works [1, 2].
physics.plasm-ph↗
On the stability of the $m=1$ rigid ballooning mode in a mirror trap with high-beta sloshing ions
Stability of the ``rigid'' $m = 1$ ballooning mode in a mirror axisymmetric trap is studied for the case of oblique neutral beam injection (NBI), which creates an anisotropic population of fast sloshing ions. Since small-scale modes with azimuthal numbers $m>1$ in long thin (paraxial) mirror traps are easily stabilized by finite Larmor radius (FLR) effects, suppression of the rigid ballooning and flute modes would mean stabilization of all MHD modes, with the exception of mirror and fire-hose disturbances, which are intensively studied in geophysics, but have not yet been identified in mirror traps. Large-scale ballooning mode can, in principle, be suppressed either by the lateral perfectly conducting wall, or by the end MHD anchors such as cusp, or by biased limiters, or by combination of these two methods. The effect of the wall shape, vacuum gap width between the plasma column and the lateral wall, angle of oblique NBI, radial profile of the plasma pressure, and axial profile of the vacuum magnetic field are studied.
physics.plasm-ph↗
Influence of the shape of a conducting chamber on the stability of rigid ballooning modes in a mirror trap
The MHD stabilization of ``rigid'' flute and ballooning modes with azimuthal number $m = 1$ in an axisymmetric mirror trap by means of a perfectly conducting lateral wall is studied both in the presence and in the absence of the end MHD anchors. Numerical calculations were carried out for an anisotropic plasma created by injection of a beam of neutral atoms into the minimum of the magnetic field at the right angle to the trap axis. The stabilizing effect of the conducting shell in the form of a straight cylinder is compared with a proportional chamber, which, on an enlarged scale, repeats the shape of the plasma column. It is confirmed that for effective wall stabilization of the rigid modes, the plasma beta ($β$, the ratio of the plasma pressure to the magnetic field pressure) must exceed some critical value $β_{\text{crit}}$. When conducting lateral wall is combined with conducting end plates imitating MHD end anchors, there are two critical beta values and, respectively, two stability zones $β<β_{\text{ crit}1}$ and $β> β_{\text {crit}2}$ that can merge, making the entire range of allowable beta values $0<β<1$ stable. The dependence of the critical betas on the plasma anisotropy, mirror ratio, and the width of the vacuum gap between the plasma and the lateral wall is examined. In contrast to the earlier works of other authors focused on to the stepwise plasma model, the stability margins are calculated for a number of diffuse radial pressure profiles with different peakedness and several axial magnetic field profiles.
physics.plasm-ph↗
Stabilization of the $m=1$ mode in a long-thin mirror trap with high-beta anisotropic plasmas
The stabilization of ``rigid'' flute and ballooning modes $m = 1$ in an axisymmetric mirror trap with the help of an ideally conducting lateral both in the presence and in the absence of end MHD anchors is studied. The calculations were performed for an anisotropic plasma in a model that simulates the pressure distribution during the injection of beams of fast neutral atoms into the magnetic field minimum at a right angle to the trap axis. It was assumed that the lateral wall has the shape of a cylinder with a variable radius, so that on an enlarged scale it repeats the shape of the plasma column. It has been found that for the effective stabilization of the listed modes by an ideally conducting lateral wall, the parameter beta ($β$, the ratio of the plasma pressure to the magnetic field pressure) must exceed some critical value $β_{\text{crit}}$. When combined with a conducting lateral wall and conducting end plates imitating MHD end stabilizers, there are two critical beta values and two stability zones $0<β<β_{\text{ crit}1}$ and $β_{\text {crit}2}<β<1$ that can merge, making the entire range of allowable beta values $0<β<1$ stable. The dependence of the critical betas on the degree of plasma anisotropy, the mirror ratio, and the width of the vacuum gap between the plasma and the lateral wall is studied. In contrast to the works of other authors devoted to the plasma model with a sharp boundary, we calculated the boundaries of the stability zone for a number of diffuse radial pressure profiles and several axial magnetic field profiles.
physics.plasm-ph↗
Wall stabilization of the rigid ballooning $m=1$ mode in a long-thin mirror trap
The prospect of stabilization of the $m=1$ ``rigid'' ballooning mode in an open axially symmetric long-thin trap with the help of a conducting lateral wall surrounding a column of isotropic plasma is studied. It is found that for effective wall stabilization, the beta parameter must exceed $70\%$. The dependence of the critical beta on the mirror ratio, the radial pressure profile, and the axial profile of the vacuum magnet has been studied. It is shown that when a conductive lateral wall is combined with conductive end plates simulating attachment of the end MHD stabilizers to the central cell of an open trap, there are two critical beta values and two stability zones that can merge, making stable the entire range of allowable beta values $0<β<1$.
physics.plasm-ph↗
On the stability of small-scale ballooning modes in mirror traps
It is shown that steepening of the radial plasma pressure profile leads to a decrease in the critical value of beta, above which small-scale balloon-type perturbations in a mirror trap become unstable. This means that small-scale ballooning instability leads to a smoothing of the radial plasma profile. This fact seems to have received little attention in the available publications. The critical beta values for the real magnetic field of the gas-dynamic trap was also calculated. In the best configuration the critical beta 0.72 is obtained for a plasma with a parabolic radial pressure profile.
physics.plasm-ph↗
On the structure of the boundary layer in a Beklemishev diamagnetic bubble
The article provides a kinetic description of the plasma equilibrium in the Beklemishev diamagnetic trap, where the traditional approach based on the theory of magnetic drifts is not applicable, since the ions move in a substantially non-circular orbit, the diameter of which is approximately equal to the diameter of the diamagnetic bubble. The ion distribution function was found in the collisionless approximation, neglecting the diamagnetic electron current. The radial profile of the magnetic field, the plasma density, the current density, and the components of the pressure tensor are calculated. It was found that the width of the boundary layer in the diamagnetic bubble varies from 6 to 8 Larmor radii calculated by a vacuum magnetic field. An adiabatic invariant is calculated that replaces the magnetic moment, which is not conserved in the diamagnetic bubble. The criterion of absolute confinement is formulated and the plasma equilibrium is found for the case when the adiabatic invariant is not conserved and only ions whose velocity satisfies the criterion of absolute confinement are trapped.
physics.plasm-ph↗
Dispersion Relation of a Surface Wave at a Rough Metal-Air Interface
We derived a dispersion relation of a surface wave at a rough metal-air interface. In contrast to previous publications, we assumed that an intrinsic surface impedance due to a finite electric conductivity of the metal can be of the same order as the roughness-induced impedance. We then applied our results to the analysis of a long-standing problem of the discrepancy between the experimental data on the propagation of surface waves in the terahertz range of frequencies and the classical Drude theory.
physics.optics↗