Measurements of the particle confinement time in the L-2M stellarator

A novel method for measuring the particle confinement time by using spectroscopic data has been developed. The electron influx into plasma is estimated from the intensity of the H_α line. The first results obtained by this method in the L-2M stellarator are discussed.     

Calculation of the charged particle source in a toroidal magnetic confinement system (hydrodynamic approach)

In order to model transport processes in magnetic confinement systems, it is necessary to have information on the charged particle source. This in turn requires calculation of the inward flux of neutral particles. In this paper, a method for solving this problem in the hydrodynamic approach for the neutral gas is proposed. The average velocity of neutral particles and the spatial distribution of their density are determined. The obtained expression for the neutral density almost completely coincides with that calculated previously by solving the kinetic equation. However, the computational time required to solve the problem in the proposed hydrodynamic approach is much shorter than that in the kinetic approach.     

Tearing instability of a force-free magnetic configuration in a collisionless plasma

The equilibrium and stability of a sheared force-free magnetic field in a collisionless plasma are investigated, and the main features of charged particle motion in such a field are analyzed. A steady solution is derived to the Vlasov-Maxwell equations for the charged particle distribution function that describes different equilibrium configurations. The tearing instability of the magnetic field configurations is studied both analytically and by particle-in-cell simulations.     

Solitary fast magnetosonic waves propagating obliquely to the magnetic field in cold collisionless plasma

Solutions describing solitary fast magnetosonic (FMS) waves (FMS solitons) in cold magnetized plasma are obtained by numerically solving two-fluid hydrodynamic equations. The parameter domain within which steady-state solitary waves can propagate is determined. It is established that the Mach number for rarefaction FMS solitons is always less than unity. The restriction on the propagation velocity leads to the limitation on the amplitudes of the magnetic field components of rarefaction solitons. It is shown that, as the soliton propagates in plasma, the transverse component of its magnetic field rotates and makes a complete turn around the axis along which the soliton propagates.     

Boundary of the adiabatic motion of a charged particle in a dipole magnetic field

The motion of a charged particle in a dipole magnetic field is considered using a quasi-adiabatic model in which the particle guiding center trajectory is approximated by the central trajectory, i.e., a trajectory that passes through the center of the dipole. A study is made of the breakdown of adiabaticity in the particle motion as the adiabaticity parameter χ (the ratio of the Larmor radius to the radius of the magnetic field line curvature in the equatorial plane) increases. Initially, for χ?0.01, the magnetic moment μ of a charged particle undergoes reversible fluctuations, which can be eliminated by subtracting the particle drift velocity. For χ?0.1, the magnetic moment μ undergoes irreversible fluctuations, which grow exponentially with χ. Numerical integration of the equations of motion shows that, during the motion of a particle from the equatorial plane to the mirror point and back to the equator in a coordinate system related to the central trajectory, the analogue of the magnetic moment μ is conserved. In the equatorial plane, this analogue undergoes a jump. The long-term particle dynamics is described in a discrete manner, by approximating the Poincaré mapping. The existence of the regions of steady and stochastic particle motion is established, and the boundary between these regions is determined. The position of this boundary depends not only on the adiabaticity parameter χ but also on the pitch angle. The calculated boundary is found to agree well with that obtained previously by using the model of a resonant interaction between particle oscillations associated with different degrees of freedom.     

Effect of the transverse magnetic field on turbulence and parameters of a plasma column in the L-2M stellarator

The influence of magnetic configurations with magnetic hills or wells on the parameters of a plasma column and turbulence characteristics were studied in experiments in which the plasma was created and heated by a microwave beam at the second harmonic of the electron cyclotron frequency. Calculations show that, for 〈β〉=(1.5?2)×10^?, a configuration with a magnetic well takes place and the Mercier criterion for stability of the ideal MHD modes is satisfied. It is shown that the compensation of the Shafranov shift of the plasma column by a transverse (vertical) field (B _v /B ₀ =5×10^?3) leads to a configuration with a magnetic hill in which the Mercier stability criterion is violated in the central region of the plasma column. It is experimentally shown that the stored plasma energy in the magnetic-hill configuration is reduced by one-half in comparison with the magnetic-well configuration. In the case of a magnetic hill, the energy of fluctuations increases both in the plasma core and near the separatrix, and the quasi-regular components of the wavelet spectra grow. When the Shafranov shift is compensated only partially (B _v/B ₀～3×10^?3) and the system is near the instability threshold, the stored plasma energy and the central electron temperature are somewhat higher, and the radiation power of fast electrons from non-Maxwellian tails at the second harmonic of the electron gyrofrequency decreases. It is found that the wavelet spectra of fluctuations change, the coherence coefficient for spectral components increases, and the radial electric field near the separatrix decreases.     

Quenching of an electric arc in a vacuum gap with a uniform transverse magnetic field

The breaking ability of a vacuum arc interrupter with a uniform transverse magnetic field formed by a system of permanent magnets was investigated experimentally. The vacuum interrupter with a 0.5-μF shunting capacitor switched off a dc current of up to 150 A at magnetic fields of 100–180 mT. At magnetic fields of 120–160 mT, the breaking ability of the vacuum interrupter was increased to 300 A by introducing a nonuniformity in the magnetic field distribution near the contact surface.     

Stability of localized MHD perturbations in confinement systems with closed magnetic field lines

Conditions are determined for the stability of a finite-pressure plasma against perturbations localized near a magnetic field line in a magnetic confinement system without average minimum-B. The marginal stability (ω²=0) is achieved at the pressure profile p∝U ^?5/3 (where $U = \oint {\frac{{dl}}{B}}$ ), provided that the pressure is lower than a certain critical value above which an unstable incompressible mode in which the displacement as a function of the coordinate along the field line has zeros appears at some magnetic field line.     

Peculiarities of collisionless drift instabilities in poloidal magnetic configurations

Results of the numerical analysis of collisionless drift instabilities as applied to magnetic configurations with a purely poloidal magnetic field are presented. Instabilities caused by the gradients of the ion and electron temperatures and plasma density are considered within a wide range of wavenumbers. An electromagnetic model taking into account the finite plasma pressure and magnetic field curvature is formulated for configurations with a nonuniform magnetic field.     

Properties of the drift trajectories of oppositely propagating particles in a stellarator with a magnetic shear

Results are presented from numerical simulations of the drift trajectories of transit particles in the L-2M stellarator by using the TRAJ computer code developed at the Prokhorov Institute of General Physics of the Russian Academy of Sciences (Moscow, Russia). Simulations show that, in a stellarator magnetic configuration with a large magnetic shear, transit ions that start from the same point of the magnetic surface and propagate in opposite directions have substantially different trajectories. Even with a simplified model of magnetic configuration, an analytical study of the ion drift motion allowed us to reveal possible underlying causes of this numerical result.     

Effect of the magnetic field on the resonant particle acceleration

The acceleration of charged particles trapped by a potential wave in a magnetic field is investigated as applied to the problem of the generation of fast particles in a laser plasma. The conditions for unlimited particle acceleration are determined, and the spectra of fast particles are found.     

Particle confinement in axisymmetric poloidal magnetic field configurations with zeros of B: Methodological note

Collisionless particle confinement in axisymmetric configurations with magnetic field nulls is analyzed. The existence of an invariant of motion—the generalized azimuthal momentum—makes it possible to determine in which of the spatial regions separated by magnetic separatrices passing through the magnetic null lines the particle occurs after it leaves the vicinity of a magnetic null line. In particular, it is possible to formulate a sufficient condition for the particle not to escape through the separatrix from the confinement region to the external region. In the configuration under analysis, the particles can be lost from a separatrix layer with a thickness on the order of the Larmor radius because of the nonconservation of the magnetic moment μ. In this case, the variations in μ are easier to describe in a coordinate system associated with the magnetic surfaces. An analysis is made of the applicability of expressions for the single-pass change Δμ in the magnetic moment that were obtained in different magnetic field models for a confinement system with a divertor (such that there is a circular null line).     

Plasma equilibrium in a double-dipole magnetic confinement system with a separatrix

Results are presented from theoretical studies of plasma equilibrium consistent with the convective stability of ideal interchange modes in axisymmetric configurations with an outward-decreasing field that may have a separatrix limiting the plasma volume. A two-dimensional numerical code is developed to solve the Grad-Shafranov equation with a convectively stable pressure distribution at an arbitrary value of β. The problem is solved for an actual geometry of the magnetic field produced by thin current rings. Configurations of a double-dipole confinement system are calculated for the parameters measured in experiments carried out in the Magnetor device, as well as for higher β values. A configuration of a model mirror system with a divertor is also calculated. The code allows one to optimize confinement systems operating at high β values at which equilibrium still can exist.     

Physical nature of the electric current produced by the asymmetry of particle motion in toroidal magnetic confinement systems

A new type of longitudinal electric current is revealed by analyzing the drift trajectories of charged particles in a tokamak—the current that may be referred to as the asymmetry current because it is associated with the asymmetry of the boundary between trapped and transit particles in phase space. The generation of this current is explained by the fact that the motions of the particles that cross the magnetic surface at a given point in opposite directions are qualitatively different. The asymmetry current results from the toroidal variations of the magnetic field and is maintained by the radial momentum flux of transit particles. The contribution of the particles of different species to the asymmetry current density is proportional to their pressure, is independent of the gradients of the plasma parameters, is maximum at the magnetic axis, and decreases toward the plasma periphery. In contrast to standard neoclassical theory, the asymmetry current can be found only from exact particle trajectories. The asymmetry current is calculated for tokamaks with differently shaped magnetic surfaces and for a model stellarator. By exploiting the newly revealed asymmetry current, together with the bootstrap current, it may be possible to substantially simplify the problem of creating a tokamak reactor.     

Effect of vacuum chamber boronization on the plasma parameters in the L-2M stellarator

After boronization of the vacuum chamber of the L-2M stellarator, radiative losses from ohmically and ECR heated plasmas were reduced by a factor of 3–4. Under these conditions, radiative losses in the ECRH regime comprise only 10–15% of the input microwave power. Some effects have been detected that were not observed previously: a substantial increase in the gradient of the electron temperature near the separatrix, a preferentially outward-directed radial turbulent particle flux (both throughout the discharge phase and from shot to shot), and a longer (by a factor of 2–3) duration of the plasma cooling phase.     

Study of plasma confinement in the L-2M stellarator during the formation of an edge transport barrier

A plasma confinement mode characterized by the formation of an edge transport barrier (ETB) was discovered in the L-2M stellarator after boronization of the vacuum vessel wall. The transition into this mode is accompanied by a jump in the electron temperature by 100–200 eV at the plasma edge and a sharp increase in the gradient of the electron temperature T _e in this region. The threshold power for the transition into the ETB confinement mode with an increased electron temperature gradient is P _thr ^?Te = (60 ± 15)n _e [10¹⁹ m^?3] kW. The formation of the ETB manifests itself also in a substantial change in the electron density profile. A density peak with a steep gradient at the outer side forms at the plasma edge. The threshold power for the transition into the ETB confinement mode corresponding to a substantial increase in the plasma density gradient near r = a is P _thr ^?Te = (67 ± 9)n _e [10¹⁹ m^?3] kW, which agrees to within experimental error with the threshold power for the transition into the ETB confinement mode determined from the sharp increase in the gradient of the electron temperature T _e . The value of P _thr for the L-2M stellarator agrees to within 25% with that obtained from the tokamak scaling. In the ETB confinement mode, the plasma energy W and the energy confinement time τ _E determined from diamagnetic measurements increase by 20–30% as compared to those obtained from the stellarator scaling for the confinement mode without an ETB. When the heating power increases by a factor of 2–3 above the threshold value, the effects related to improved energy confinement disappear.