No abstract

An efficient algorithm is proposed enabling numerical simulations of plasma dynamics in a nonuniform magnetic field. The present numerical data are in good agreement with experimental data obtained in a GOL-3 setup and with previous simulations. The experimentally observed effect of fast transfer of energy to ions is confirmed.Introduction. In GOL-3 experiments on plasma heating and confinement in a multiple-mirror trap, fast heating of plasma is ensured by a relativistic electron beam with an energy up to 1 MeV (current up to 30 kA, duration up to 8 µsec, and energy up to 120-150 kJ) [1]. A deuterium-plasma column of density n ≈ 10 15 cm −3 , length of 12.3 m, and diameter of 4-5 cm is formed in a corrugated magnetic field consisting of 55 cells, each 22 cm long, with a magnetic ratio B max /B min = 5.2/3.2 T. The plasma column is confined by edge magnetic mirrors with a magnetic field of B max ≈ 9 T. Collective heating of the plasma by the beam proceeds under conditions of developed Langmuir turbulence and lengthwise electron heat conduction being suppressed by turbulent electric fields; in the corrugated field, such a situation gives rise to periodic longitudinal modulation of the electron temperature and pressure. The pressure gradient initiates formation and acceleration of plasma flows toward the centers of magnetic cells. Experiments showed that collisions between the flows result in neutron outbursts of thermonuclear nature, followed by fast thermalization of the directional energy of plasma motion accompanied by neutron emission [1]. Measurements confirmed a fast growth of ion energy (up to 1-2 keV for the period of beam action), which could not be explained by the Coulomb electron-ion collisions. To investigate the above-mentioned mechanism of fast transfer of energy to ions, the dynamics of a two-component plasma was numerically simulated in [2] with the use of traditional computational algorithms [3] in the hydrodynamic approximation, because the ion temperature in the plasma generated by a direct discharge in deuterium is low at the initial stage of heating and the free path of ions is much shorter than the length of one cell in the multiple-mirror trap. As a numerical analysis showed and an experiment confirmed [1], the dynamics of the plasma under such conditions is accompanied by generation of high-amplitude nonlinear waves, which requires more efficient algorithms to be developed to model the process of interest.To numerically solve strongly nonlinear problems, algorithms with enhanced stability, capable of predicting solutions over long time intervals, are required (see [4]). Such algorithms can be developed on the basis of predictorcorrector schemes, where the required stability is ensured at the predictor stage and conservatism is re-established at the corrector stage, thus providing for satisfaction of differential conservation laws. A predictor-corrector scheme was proposed in [5,6] for the numerical solution of gas-dynamic equations. The technique of splitting in terms of physical processes...

A model of dynamics and heating of a plasma cloud in a magnetic field is considered in a twotemperature approximation. Based on a predictor-corrector-type implicit difference scheme, spreading of a plasma cloud in an external magnetic field is numerically simulated, and the influence of this field on spread dynamics is evaluated. Introduction.In experiments on plasma heating and confinement in a multiple-mirror trap in a GOL-3 setup, rapid heating of the plasma can be ensured by using a relativistic electron beam. Experiments demonstrated that the electron component of the plasma is heated under conditions of a developed Langmuir turbulence suppressing electron-type heat conduction. Rapid heating of ions in the plasma to a temperature commensurable with the electron temperature is observed thereby. This heating can be attributed to a collective character of ion acceleration under the gradient of the electron pressure of the plasma rather than to electron-ion collisions [1,2]. To study the above-described mechanism of fast transfer of energy from electrons to ions, Arzhannikov et al. [3] and Astrelin et al.[4] modeled the dynamics of a two-component plasma in a one-dimensional hydrodynamic approximation by different numerical methods. Numerical and experimental results show that plasma motion under these conditions is accompanied by emergence of high-amplitude nonlinear waves. This required a special numerical method to be developed [4,5], which would be stable in a wide range of plasma parameters and sufficiently accurate for solving problems of this class.A refined two-dimensional model is proposed in the present paper to describe the motion of a one-fluid two-temperature plasma with allowance for the effects of heat conduction, electrical conduction, thermal forces, and friction forces arising in collisions between ions and electrons. A predictor-corrector-type implicit difference scheme was proposed for the numerical solution of magnetohydrodynamic problems in one-dimensional and multidimensional approximations [5,6]. This model is extended below to the case of a two-temperature plasma. The problem of spreading of an originally spherical hot plasma cloud under the action of hydrodynamic forces and a magnetic field is solved. At the present stage of research, dissipative effects are neglected, but it is assumed that the initial ion and electron temperatures may be different. The influence of an external magnetic field and initial temperature distribution within wide ranges of their values on the characteristics of plasma motion is studied.Physicomathematical Model. The problem of propagation of a dense plasma cloud in an external magnetic field is considered. The original plasma cloud is assumed to have a spherical shape and to have parameters (pressure, density, and temperature) whose values are several orders higher than the background level. Under the action of hydrodynamic and magnetic pressures, this cloud starts spreading over the background plasma. The flow is assumed to be axisymmetric and is simulated ...

No abstract