The authors consider the interaction of a plasma column in a constant magnetic field H z with a system of two counter-rotating high-frequency magnetic fields whose axis of rotation is directed along a constant magnetic field. Both the first and the second wave are uniform along the axis of rotation. The configuration of the high-frequency field is such that the electrical component of the field is directed along the constant magnetic field, while the latter does not influence the effectiveness of the action of the high-frequency field on the plasma.It is assumed that the collision frequency v of the charged particles in the plasma is non-zero. Taking into account entrainment of the plasma by the high-frequency field, one can use -instead of the second wave of the alternating field -the constant magnetic field of a multipole configuration, which behaves as a high-frequency field relative to the rotating plasma. The distribution of the plasma rotation velocity v the charged particle concentrations N and the strength of the alternating fields £L, and ff r along the plasma column radius are determined by a system of Maxwellian equations and equations of motion for the ions and electrons. A system of equations with boundary conditions is solved by computer, and the radial dependences of the angular velocity of rotation, the plasma concentration and the high-frequency fields for different values of the multipole magnetic field and the plasma concentration are ascertained. If the ratio of the field strengths at the plasma boundary is of the order of unity, then the plasma column has a tubular structure.In the case of a rotating plasma, the radial distribution of the high-frequency field is of a peculiar type.
The authors consider the equilibrium of a toroidal plasma pinch in a constant magnetic field on which is superposed a helical high-frequency field produced by helical currents flowing on a toroidal surface with major radius R and minor radius rk. The helical currents are proportional to exp[i(ωt – nψ – k‖ζ)], where ω is the frequency imparted by the generator, ψ the polar angle in the meridional cross-section of the torus, and ζ is the length of arc along the major circumference of the torus. The authors demonstrate that it is possible to achieve equilibrium with high-frequency field pressures less than the kinetic pressure of the plasma. An expression is derived for the displacement of the pinch in the equilibrium state as a function of high-frequency field amplitude, plasma kinetic pressure, the multipolarity n, and such geometric parameters as the radius of the plasma pinch rp, the radius of the circuit rk and the radius of the torus R. In the helical high-frequency field, the equilibrium of the plasma pinch depends to a great extent on the strength of the constant magnetic field H0, the plasma concentration N, the frequency of the variable field f = 2π/ω, and the wavelength of the helical current λ‖ = 2π/k‖. The helical high-frequency electromagnetic field within the plasma is a superposition of two wave types. When H0 < Hcrit = the first type of wave transfers to the skin, and when H0 > Hcrit. it propagates. When k‖rp ≪ 1 and k‖rp ≪ H0/Hcrit. the field of the second type of wave differs only slightly from the vacuum field. In the region where the first type of wave transfers to the skin, the displacement Δ of the plasma pinch decreases with increasing H0 and becomes zero when H0 = Hres = : with further increases in the magnetic field strength Δ becomes negative. H0 = Hres is the condition for resonance excitation of the helical high-frequency field within the plasma. The most effective use of high-frequency power for equilibrium containment of the plasma pinch within the torus is to be expected near this resonance on the side where Δ > 0. The change in the sign of Δ is a consequence of a change in the direction of the force acting on the plasma. If there are two types of wave in the plasma, there appear – in addition to the forces associated with the pressure of each individual wave -forces produced by the interaction of the currents excited by one wave type with the field of the other wave type, and vice versa. For certain parameter values, the phase relations of the fields and currents may be such that the additional forces associated with the cross interaction may work in a direction opposite to that of the forces produced by the pressure of each individual wave. In the propagation region of the first wave, i.e. where H0 > Hcrit. positive and negative values of the plasma pinch displacement alternate (i.e. there are alternating regions of stable and unstable equilibrium respectively).
The authors consider the equilibrium of a toroidal plasma column in a steady-state magnetic field on which is superimposed a multipole high-frequency field produced by currents flowing around the major circumference of the torus which are proportional to exp[i (ωt-nψ)], where ψ is the polar angle in the meridional cross-section of the torus and ω is the frequency determined by the generator. They demonstrate the possibility of achieving equilibrium when the pressure of the high-frequency field is less than the kinetic pressure of the plasma, ignoring the reaction of the circuit to the displacement of the plasma column; i.e. it is assumed that this displacement does not give rise to image currents in the circuit. An expression is derived for displacement of the column as a function of the amplitude of the high-frequency field, the kinetic pressure of the plasma, the depth of the skin layer, the multipole order (n), and of geometric parameters such as the radius of the plasma column rp, the radius of the circuit rk and the radius of the torus R. The displacement of the column is proportional to the kinetic pressure of the plasma, inversely proportional to the square of the amplitude of the current in the circuit, and independent of the steady-state magnetic field. Expressed as a function of the multipole order (n), displacement is at a minimum when n is equal to the whole number closest to 1 + [1/2 ln(rk/rp)]. When rk/rp∼2, the optimum value of n is 2 (quadrupole). When n = 1 (dipole), displacement increases in proportion to ln(c/ωrp). On the assumption of a quasi-steady state (c/ωrp ≫ 1) equilibrium containment of the plasma in the dipole case is found to be difficult to achieve in practice. When n = 0 equilibrium is quite impossible to achieve. The validity of this conclusion is dependent on the assumption of a quasi-steady state and on the further assumption that the circuit will not react to displacement of the column.
The paper considers the interaction of a high-frequency electromagnetic field with a magnetized inhomogene-ous plasma. From kinetic and Maxwellian equations a system of equations is obtained which describes the linear oscillations of an inhomogeneous plasma. The dispersion relation is given for the potential oscillations. The results are obtained for the limiting case of long waves k⊥ρΛ→0. Three types of drift instability are considered: (a) electronic drift instability; (b) slow ion-acoustic waves, and(c) drift-temperature instability.It is shown that, by applying an h.f. field having a certain frequency and intensity it is possible to enlarge the region of stability against drift oscillations in an inhomogeneous magnetized plasma.When an h.f. field is applied, the stability region for a fast ion-acoustic wave grows considerably in the direction of negative values of ηe. Stabilization occurs as a result of the increased oscillation frequency which accompanies the application of the h.f. field, and this in turn intensifies Landau damping by the electrons.The stabilizing effect of the h.f. field pressure is associated with a Doppler shift resulting from plasma particle drift with velocity g/ωHα (g is the effective ‘acceleration due to gravity’ with allowance for the potential forces in a non-perturbed state). The sign of the growth rate of the slow ion-acoustic wave does not change when the h. f. field is applied, but its value decreases considerably. The h.f. magnetic field stabilizes the drift-temperature instability for negative values of ηi.
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