INSTITUTE OF PLASMA PHYSICS

NAGOYA UNIVERSITY

On Steady Operation of Field Reversed Configurations

Kazunari IKUTA (Recieved June 19, 1979)

IPPJ-400 June 1979

RESEARCH REPORT

NAGOYA, JAPAN On Steady Operation of Field Reversed Configurations

Kazunari IKUTA (Recieved June 19, 1979)

IPPJ-400 June 1979

Further communication about this report is to be sent to the Research Information Center, Institute of Plasma Physics, Nagoya University, Nagoya 464, Japan ABSTRACT

A new method of sustaining toroidal current by the use of energetic ions in field reversed mirror configuration is considered. Since no charge-neutralizer is required in this method, the reactor system will be drastically simplified. Once field reversal is achieved in a magnetic mirror, the distinction between a torus and a mirror vanishes. Historically the first proposed field reversed configuration is the astron , where electrons gyrate in an axially symmetric magnetic field, thereby creating a current layer known as the E-layer. The electric currents from this layer, together with currents in external windings, produces the magnetic field which confines the electrons. Under a certain condition, a faiaily of closed field lines are generated. This closed magnetic lines can act as a cage to confine a plasma for thermonuclear purpose, providing that the gyrating electrons have long life and that the system is stable. In this kind of magnetic configuration the plasma is stable as long as the current generated by an E-layer of

axis-encircling electrons and ions is stable, since the 2) plasma sits in a magnetic well dug by the E-layer , The field reversed mirroir'is topologically similar to the astron system although the current-carrying particles do not encircle the axis. In this system no magnetic well effect can be expected, i.e. plasma cannot be stabilized by a magnetic well dug by itself. One of clever ways to stabilize plasmas in a field reversed mirror is to add a toroidal field in order to have shear in the configuration without use of toroidal field coil '. In both configurations a problem is how to maintain such a system of f:elds and currents in an isolated volume of plasmaJ Many people have given the ideas for steady operation

- 1 - of standard tokamaks by the use of neutral beams and the relativistic electron beam. These ideas might also be useful for the reversed field configurations.

A disadvantage of using neutral beam for current sustaining is to generate an energetic neutral beam of order 200 keV against a small efficiency of charge neutralizer. In the case of using relativistic electron beam for the same purpose, toroidal magnetic field is inevitably required in order to form relativistic electron beam ring for current sustaining. Since the toroidal field is absent in field- reversed mirror outside the plasma the application of electron beam method for current sustaining is impossible to this case.

The absence of toroidal field outside the plasma in reversed field configurations, however, enables us to accurately inject energetic ions through the throats of mirror across the closed magnetic surfaces in order to give momentum to electrons although the time of flight of the ions across the magnetic surfaces is rather short. A schematic drawing of a reversed field configuration with toroidal field in the plasma is shown in Fig.l, where energetic ions which do not encircle the axis are injected near a mirror throat and they propagate toward the other throat.

During the passage across the field-reversed region, ions encircle the axis transfering their angular momentum to the trapped electrons there by Coulomb collisions. The orbit in this region is like a double helix as shown with exaggerations. Near the other mirror throat the propagating ions are reflected by mirror effect. In this way ions can oscillate

- 2 - between the mirror points until they are scattered into the loss cone of the mirror field. If ions can oscillate many times between the mirror throats, the energetic ions are able to propel electrons in the toroidal direction by collisions in order to sustain the reversed field configuration. The purpose of the present note is to consider a problem of current sustaining in the field reversed configurations with toroidal field by the use of energetic ions oscillating between mirrors. We use standard cylindrical coordinate system (r,6, z). In axisymmetric magnetic field the canonical angular momentum is conserved during a particle motion.

Mrve + e¥ = const , (1)

where v0 is the 9 component of the velocity and f is defined by f = rA- (A. being the 0 component of the vector potential). To fascilitate physics understanding we hereafter assume that f < 0 in the region of field reversal. For

the initial conditions, vQ = 0 and ¥ = ¥0 > 0 , at the injection point, the equation (1) is reduced to

v e Mr ll)

This means that |v_| increases if the ion enters the region of field reversal. By a choice of the parameters the injected ions does not encircle the axis in the region of positive V. In this case the motions of axis-encircling can be expected for the ions when they enter the region of field reversal, i.e. the region where V < 0. In this region a dense plasma

- 3 - is assumed to be contained so that the collisions between the energetic ions injected and the background electrons possibly occur, although the transit time, T, of the ions between mirrors through the region of negative V! should be still sufficiently shorter than the slowing down time, T , of the energetic ions, i.e. the electrons can receive momentum from ions,though the ion motion can be assumed not to be severely influenced by the momentum transfer.

The momentum transfer, AP, from ions during a crossing through the region of field reversal can roughly be estimated using(2) as follows.

(3)

where N^ is the number of energetic ions and t represents the time. We note here that the electrons which receive momentum from ions are driven in the direction of the paramagnetic current along lines of force because the ions encircle the axis in the diamagnetic direction. Since ions travel N times between mirrors until they enters the loss cone of the mirror field, the increase of electron velocity, Au, by the momentum transfer can be written by

where m is the mass of an electron and Ne the number of electrons which encounter ions. The electrons can travel along field lines which form a family of the closed nested - 4 - magnetic surfaces. If the injection point of the ions is chosen properly, the ion orbit could cross the magnetic axis in the reversed field configuration, where the magnetic axis satisfies the condition -r1- = £=• = 0 together with r / 0. or o u In this case the momentum supply to electrons from the energetic ions can be completed throughout the magnetic surfaces which form the reversed field region. The increment of total current, AI, by the momentum transfer can be written by N ?e Au ' (5"a) where R corresponds to the distance between the Z axis and the magnetic axis. The relation (5-a) can be reduced to, together with (3) and (4),

N e2 ;T N AT ~ i Yo-¥ ,. ,c ,. AI = «R 1ST- "r— dt * (5~6)

The time dependence of toroidal current of a resistive plasma in a reversed configuration should be decribed by

I = IQ exp( - -i- ) , (6) where x is a time constant of the current decay and IQ the initial current intensity. In a time duration, At, the decrement of the toroidal current (AI) is written by

(Ai)* = - -L ^ . (7)

- 5 - The decrement is fully compensated by the momentum transfer from the injected ions. Then we have

AI + (AI)* = 0 , (8-a)

N e2 fT ¥ -v I At „ N _^_ _o_ dt m (8_b) WH mTs j Q r

Since ions are assumed to travel N times between mirrors until they enter the loss cone of the mirror field At should be rewritten by

At = 2NT = TS . (9) Using the relation (9) the necessary number of ions in order to sustain the toroidal current of the configuration is obtained by (8-b).

(10)

Very roughly r can be thought of as a constant and V - ¥ =B r2, where B is an axial field for the equilibrium of toroidal current. Then we have

Ni a ? < "T > 4 where u = eB /m and r a R. For a set of parameters, i.e. B = 5 Tesla, I = 6 * 106

- 6 - Ampere, R = 0.1 meters, x = 10*" sec and T = 0,5 sec (this value of T correspond to the ion energy 10 MeV and the s 14 T*3 plasma density of order 10 cm }, total ion number N^ becomes

16 Nf = 1.2 x 10

In other words the necessary ion current, I., for one burst must be

i is

= 4 x 10" Ampere

in order to complete the current sustaining. Although the necessary current of the ions is moderately small, the energy of 10 MeV sounds rather high. In order to generate the ion beams with energy of order 10 MeV we may utilize a technique of adiabatic magnetic compression. Initially a pulse of a few MeV ions is injected into a small mirror which is formed near the main mirror throat. By adiabatic compression of the ions in a small mirror field the ion energy is increased, proportional to the field intensity, to about 10 MeV. By opening the gate of the small mirror field a burst of ions can be easily injected towards the region of field reversal.

Once the field-reversed configuration is formed in a mirror field, we may conclude from the above considerations that the current sustaing in an isolated volume of plasma in the configuration is possible by the use of energetic

- 7 - ion beams. Since the complicated charge-neutralizing process of the neutral beam technology is not necessary in the new reactor system described heref the maintenance of the system would be drastically simplified.

- 8 - References

1) N.C. Christofilos: Proceedings of the Second International Conference on Peaceful Uses of Atomic Energy (United Nations, Geneva, 1958), Vol. 32, p,279.

2) R.V. Lovelace: Phys. of Fluids 1£ (1976) 723; see also R.N. Sudan and M.N. Rosenbluth: Phys. of Fluids 22 (1979) 282.

3) See, for example, W.C. Condit, T.K. Fowler, and R,F, Post, Lawrence Livermore Laboratory Report No. UCRL-52170 (1976),

4) M.N. Bussac, H.P. Furth, M, Okabayashi, M.N, Rosenbluth, A.M. Todd: Plasma Physics and Controlled Nuclear Fusion

Research (Proc. 7th Int. Conf, Innsbruck, 1978) Vol,3f to appear. See also K. Ikuta: J.J.A.P. 1]_ (1978) 1831

5) T. Ohkawa: Nuclear Fusion 10 (1970) 185; see also K. Ikuta: J.J.A.P. 11 (1972) 1684.

- 9 - Figure Caption

Schematic drawing of a reversed field configuration with toroidal field, The toroidal current of the configu- ration is sustained by energetic ion beam which is injected near the throat in such a way that the injected ions do not encircle the axis. After they enter the region of field reversal they encircle the axis. The ions travel many times between the throats of mirror field. Region of Particle Orbit Field-Reversal Injection Magnetic Surfaces Point Lines of Force

Throat of Mirror