Small Larmor Radius Limit Research Articles

Collisionless particle dynamics in trap sections with helical corrugation

Collisionless particle dynamics in a helical magnetic mirror is investigated by methods of the Hamilton dynamics. In the limit of small Larmor radius, the Hamiltonian is fully integrable and particle trajectories can be divided into three types, differing in the direction of the drift velocity. The structure of the trajectories of resonant particles and the width of the resonance are studied. The influence of weak axi-symmetrical corrugation on the particle dynamics and efficiency of plasma flow suppression through a helical mirror are discussed.

A new quasilinear formulation for ICRF plasmas in a toroidal geometry

We present a new formulation for quasilinear velocity space diffusion for ICRF plasmas that considers two different aspects: (1) finite Larmor radius approximation and (2) includes the effect of toroidal geometry and constructs a positive definite form. In the first aspect, the Kennel-Engelmann (K-E) quasilinear diffusion coefficients are successfully approximated in a small Larmor radius limit and implemented for the numerical codes (TORIC-CQL3D). In the second aspect, the quasilinear diffusion is reformulated in a toroidal geometry in order to include the parallel dynamics in the inhomogeneous plasmas and magnetic fields. We use these two quasilinear formulations to simulate ITER plasmas with ICRF injection for minority fundamental heating and Tritium second harmonic cyclotron heating.

Velocity boundary conditions at a tokamak resistive wall

Velocity boundary conditions appropriate for magnetohydrodynamic simulations have been controversial recently. A comparison of numerical simulations of sideways wall force in disruptions is presented for Dirichlet, Neumann, Robin, and DEBS boundary conditions. It is shown that all the boundary conditions give qualitatively similar results. It is shown that Dirichlet boundary conditions are valid in the small Larmor radius limit of electromagnetic sheath boundary conditions.

Investigation of tearing instability using GeFi particle simulation model

The gyrokinetic (GK) electron and fully kinetic ion (GeFi) simulation model of Lin et al. [Plasmas Phys. Controlled Fusion 53, 054013 (2011)] has been thoroughly benchmarked and validated for a two-dimensional (2D) Harris current sheet with a finite guide field. First, a gyrokinetic eigenmode theory for the collisionless tearing mode in the small Larmor radius limit is presented. The linear eigenmode structure and growth rate of the tearing mode obtained from the GeFi simulation are benchmarked against those from the GK eigenmode analysis in the limit of L≫ρi>ρe, where L is the current sheet half-width, ρi is ion Larmor radius, and ρe is electron Larmor radius. Second, to valid the GeFi model, both the linear and nonlinear tearing instabilities obtained from the GeFi simulations are compared with the Darwin particle-in-cell (PIC) simulation. The validation of the GeFi model for laboratory and space plasmas is also discussed. Meanwhile, the GeFi simulation is carried out to investigate both the linear and nonlinear tearing instabilities for cases with a broad range of L and guide magnetic field BG. It is found that in a wide current sheet with L > 4.5ρeK, the nonlinear saturation level of the island half-width is ws ≃ 3ρeK, where ρeK = ρeB0/Bx0, B0 is the strength of the asymptotic magnetic field, and Bx0 is the antiparallel field. On the other hand, in a thin current sheet with L < 2.5ρeK, ws ≃ 2.2 L. In addition, a high frequency electrostatic drift mode is found to coexist with the tearing mode.

Anisotropic Z-pinch equilibria and their stability

The Chew–Goldberger–Low equations are used to study the effect of pressure anisotropy on Z-pinches operating in the collisionless regime. The limitations on the form of accessible equilibria are investigated. The effect on the m=0 instability is asessed both by means of the energy principle and by direct solution of the eigenvalue equation for a variety of anisotropic equilibria. The results indicate that in the small Larmor radius limit pressure anisotropy offers a rather slight enhancement of the linear stability of the Z-pinch.

Small Larmor radius limit for a warm relativistic electron fluid

A fluid model is considered for a relativistic warm plasma, obtained with a closure approach that allows for a nonvanishing heat tensor. A small Larmor radius limit is assumed and a simplified magneto-fluid model that generalizes the relativistic Chew–Goldberg–Low model [Proc. R. Soc. London Ser. A 236, 112 (1956)] is obtained.

Theory and simulation of the Rayleigh-Taylor instability in the large Larmor radius.

The theory and first nonlinear simulations of the Rayleigh-Taylor instability in the limit of large ion Larmor radius are presented. It is shown that in the limit of large Larmor radius, the Rayleigh-Taylor instability evolves much faster and in a dramatically different manner than in the limit of small Larmor radius.

Small-signal analysis of the induced-resonance electron-cyclotron maser.

The induced-resonance electron-cyclotron maser operates at Doppler-upshifted frequencies \ensuremath{\omega}\ensuremath{\simeq}${\ensuremath{\gamma}}^{2}$${\ensuremath{\Omega}}_{0}$, with \ensuremath{\gamma} the relativistic factor and ${\ensuremath{\Omega}}_{0}$=${\mathrm{eB}}_{0}$/\ensuremath{\gamma}mc. In addition, the mechanism is insensitive to the beam thermal spreads when the index of refraction n=${k}_{z}$c/\ensuremath{\omega} is properly adjusted. A set of simplified equations, describing the electron dynamics near the axis of the configuration, is derived in the limit of small Larmor radius. The linear efficiency is derived for radiation having a Gaussian profile and propagating at an angle \ensuremath{\alpha} relative to a constant external magnetic field. The start-up current for operation in the submillimeter regime is well within the capabilities of today's long-pulse relativistic electron beams.

Trajectory of Charged Particles in Weakly Inhomogeneous Magnetic Fields

The detailed time dependence of the trajectory, and particularly of the acceleration, of a charged particle moving nonrelativistically in a weakly inhomogeneous, slowly varying electromagnetic field is calculated by a method that involves superimposing a conventional perturbation expansion in the weak field on the expansion of Berkowitz and Gardner and of Kruskal, the latter expansion being asymptotically valid in the limit of small Larmor radius and slowly varying fields. Fourier transforms are introduced to facilitate isolation of rapidly varying terms from the most general solutions for the coefficients in the expansion. The calculations are carried to first order in the weak inhomogeneity and (at least formally) to all orders in Larmor radius. The resulting velocity reproduces the familiar transverse drift velocities of first-order orbit theory, emphasizes that in the presence of fields varying slowly in time the polarization and curvature drifts are to be calculated from the time derivative of the fields as seen from a frame of reference fixed with respect to the guiding center of the particle's orbit, and permits calculation of higher-order contributions to the drift velocities, contributions of second order in Larmor radius being explicitly evaluated; the resulting acceleration prepares the way for a study of the effect of weak inhomogeneities on the radiative output of single particles.

Stability of Sheet Pinch

The growth rate of the sheet pinch instability is calculated in the small Larmor radius limit using the method of integration along unperturbed orbits. It is found that the instability is driven by a small group of ``resonant'' electrons which cross and drift about the neutral plane having zero velocity along the field lines. The microinstability is absolute and develops fastest for a critical perturbation wavelength, of the order of several times the thickness of the plasma sheet.

Some Stable Plasma Equilibria in Combined Mirror-Cusp Fields

The problem of equilibrium and stability of plasma confined in certain magnetic fields of combined mirror-cusp form is discussed. These fields have the properties that they are nowhere zero and everywhere increase toward the periphery. Attention is drawn to the importance of the existence of closed surfaces of constant |B|—the magnetic isobars. The conditions for plasma equilibrium are derived and interpreted; then by exploiting the existence of closed magnetic isobars certain low-β confined equilibria are constructed. These equilibria are shown to be stable according to the fluid (double adiabatic) energy principle and according to the small Larmor radius limit theory. A direct proof of stability against motions which preserve the magnetic moment is given. These equilibria have the property that there is no current along lines of force so that they are also immune to several drift instabilities.

Theoretical Structure of Plasma Equations

In high-temperature plasmas, collisions are very infrequent. Thus the charged particles travel on independent orbits determined by the electromagnetic field. At first sight this would seem completely different from a conventional fluid where particles are closely hemmed in by their neighbors. However, there can exist collective modes of motion in which the particles interact with each other by altering the fields. In this paper a new method is developed for the solution of the linearized transport equation. By facilitating direct use of the properties of particle orbits, a considerable simplification is achieved. In particular, a variational expression is derived for determining stability which is rigorous in the limit of small Larmor radius.