Consider a system made up of hydromagnetic wave and the slowly varying background fluid in which it propagates. It is shown that both effect on may be derived from Hamilton's principle using averaged Lagrangian density. The waves propagate adiabatically, conserving action, act via pressure term. Total momentum, angular energy are conserved. When many superimposed, as weak turbulence, kinetic equation replaces adiabatic conservation equation. accuracy averaging approximation examined,...

A WKB formalism for constructing normal modes of short-wavelength ideal hydromagnetic, pressure-driven instabilities (ballooning modes) in general toroidal magnetic containment devices with sheared fields is developed. No incompressibility approximation made. dispersion relation obtained from the eigenvalues a fourth-order system ordinary differential equations to be solved by integrating along line force. Higher-order calculations are performed find amplitude equation and phase change at...

Numerical simulations of ion temperature gradient (ITG) mode transport with gyrofluid flux tube codes first lead to the rule that turbulence is quenched when critical E×B rotational shear rate γE−crit exceeds maximum ballooning growth rates γ0 without [Waltz, Kerbel, and Milovich, Phys. Plasmas 1, 2229 (1994)]. The present work revisits reformulated in terms Floquet modes which convect angle. This new formulation avoids linearly unstable “box modes” from discretizing angle illustrates true...

The Hasegawa-Wakatani equations, coupling plasma density, and electrostatic potential through an approximation to the physics of parallel electron motions, are a simple model that describes resistive drift wave turbulence. Numerical analyses bifurcation phenomena in presented, provide new insights into interactions between turbulence zonal flows tokamak edge region. simulation results show regime where, after initial transient, is suppressed flow generation. As parameter controlling strength...

The time asymptotic distribution functions corresponding to adiabatic and sudden excitation of an electrostatic wave are calculated. These distributions compared used calculate the nonlinear response plasma, Poisson's equation is find a dispersion relation.

A new formulation of the quasilinear theory weakly turbulent plasmas is presented, which explicitly separates resonant and nonresonant wave-particle interactions from outset. This achieved by making a canonical transformation to “oscillation center variables” before attempting solve Vlasov equation. systematic method constructing generating function any order in wave amplitude based on variant Hamilton-Jacobi perturbation theory. Momentum energy split naturally into particle component. The...

The magnetohydrodynamic stability of a straight plasma column with elliptic cross section, carrying uniform axial current, is investigated by extremizing the Lagrangian system using natural coordinate based on magnetic field lines. Stability criteria are derived and growth rates obtained analytically for systems mass density inside plasma. It shown that coupling between kink modes Alfvén waves produced noncircularity destabilizing effect. A technique solving problem numerically also...

We describe the construction of stepped-pressure equilibria as extrema a multi-region, relaxed magnetohydrodynamic (MHD) energy functional that combines elements ideal MHD and Taylor relaxation, which we call MRXMHD. The model is compatible with Hamiltonian chaos theory allows three-dimensional equilibrium problem to be formulated in well-posed manner suitable for computation. energy-functional discretized using mixed finite-element, Fourier representation magnetic vector potential geometry;...

The critical β for stability against ideal hydromagnetic internal ballooning modes as a function of the toroidal mode number, n, is calculated two different equilibrium sequences by use finite-element technique (n ≲ 20), and WKB formalism ≳ 5). agreement between methods good in overlap region 5 n 20. formula reduces to '1/n correction' at very high but much more accurate moderate n. critical-β-versus-n curves exhibit oscillatory structure low both lower bound on βc set = ∞ about ∼ 5%.

A variational principle is proposed for constructing equilibria with minimum energy in a toroidal plasma. The total minimized subject to global invariants which act as constraints during relaxation of the These integrals motion are preserved exactly all ideal motions and approximately wide class resistive motions. We assume, specifically, that plasma dominated by tearing mode single helicity. Equilibria realistic current density pressure profiles may be constructed this theory, also used...

A coherent Alfv6n wave propagating along the equilibrium magnetic field is unstable against decay into an traveling in opposite direction and a sound (Sagdeer Galeev, 1969). The stability of incoherent waves this mode considered, assuming that are damped. criterion for stabilizing with power spectral density In ok -N N > 1. results indicate solar wind stable wavelength range considered Mariner 5 ob- servations, although mild instability predicted longer wavelengths. According to...

As a simple model for investigating the stability of an electrostatic plasma wave with trapped electrons, is regarded as nonlinear, dispersive dielectric. A non-linear Schr\"odinger-type equation found, which predicts instability both electron waves and ion acoustic waves. These instabilities do not depend on resonance bouncing motions thus have different physical origin than those predicted by bunched-beam models.

A Lagrangian, for the slowly varying complex amplitude of an almost monochromatic electrostatic plasma wave in unmagnetized plasma, is derived. The method a variant averaged Lagrangian technique Whitham, adapted use physics by employing Low's together with certain elimination procedures to simplify usable form. expansion powers carried out quartic terms, and non-adiabatic terms are also retained. Variations respect lead nonlinear Schrödinger equation amplitude, while variations particle...

A canonical transformation which removes the coherent oscillatory motion of a particle in stochastic potential (the renormalised oscillation-centre transformation) is constructed by new classical perturbation method using Lie operators and Green function techniques. frequency wavevector dependent particle-wave collision operator calculated explicitly for stationary, homogeneous electrostatic turbulence short wavelength limit. The width resonance proportional to one-third power quasilinear...

A variational principle is proposed for constructing equilibria with low free energy in toroidal plasmas which relaxation dominated by a tearing mode of single helicity. States current density vanishing on the boundary are constructed. Theoretical predictions compared experimental data from reversed field pinches and tokamaks.

The global asymptotic matching equations for multiple coupled resistive modes of arbitrary parity in a cylindrical plasma are derived. Three different variational principles given the outer region data, while inner analysis features careful treatment symmetry-breaking effect gradient equilibrium current zero-β slab model. It is concluded that usual constant-ψ result remains valid and constrains matrix formalism. dispersion relation compared with initial value calculations double tearing mode...

In specific cases, the critical beta (βc) for stability against internal magnetohydrodynamic (MHD) ballooning modes can be improved significantly by taking into account stabilizing influence of ion diamagnetic drifts. This kinetic modification to ideal MHD analysis and radial corrections local theory are included in a calculation βc as function toroidal mode number (n) particular tokamak equilibrium sequence interest.

The amplitude at which a single unstable Langmuir or ion-acoustic wave in collisionless plasma saturates due to electron trapping is estimated using both the adiabatic and sudden approximations, shown obey approximate relation ωb∼3γlin. This found from momentum conservation. It that energy conservation implies nonlinear dispersion linearly independent of derived Poisson's equation, but reasonable distribution resonant particles can be satisfies relations.

Ideal magnetohydrodynamics (IMHD) is strongly constrained by an infinite number of microscopic constraints expressing mass, entropy and magnetic flux conservation in each infinitesimal fluid element, the latter preventing reconnection. By contrast, Taylor relaxation model for formation macroscopically self-organized plasma equilibrium states, all these are relaxed save global fluxes helicity. A Lagrangian variational principle presented that leads to a new, fully dynamical, (RxMHD), such...