Dynamic stabilization of helical modes by high-frequency fields and by automatic control system in a plasma column

A study is made of the stability relatively to an excitation of helical modes of a magnetized plasma column with a homogeneous in cross-section longitudinal current. The presence of a stabilizing HF field an automatic control system makes it possible to record and amplify separately each space-time harmonics. The dispersion equation is derived and analyzed. A model of a right cylinder is used in calculations. Conditions of complete stabilization of the helical instability and required parameters of HF field and automatic control system are determined. From estimations it follows that at W0 = 1, Rsub(+1) = Rsub(-1)=10, (b/a)=1.2-1.3 M = 3, m = 1-2 amplitudes of HF critical field pairs ranges from 1/7 to 1/2. Here W is the reflection coefficient; Rsub(-1) is the gain of a difference harmonics; Rsub(-1) is the current gain of the sum harmonics; M and m are perturbation modes; a is the radius of the torus, and b is the radius of the helical contour surface. A possibility is considered of the helical instability stabilization by means of the dipole winding, which ensures the toroidal equilibrium of the plasma column. It is pointed that the most dangerous perturbation modes with m = 1.2 can be completely stabilized if the difference harmonic gain Rsub(-1) = 20 and the critical HF field hsup(cr)sub(2) = 1/80-1/160