A Plan to Reclaim Deuterons Escaping from the Loss Cone of a Magnetic Mirror

Research on magnetic mirror reactors has had two serious problems since the beginning stage. One is the magnetohydrodynamic instability due to the negative curvature of the magnetic field lines around the center region of a mirror bottle. Another is the loss of charged particles escaping from the loss cone of a magnetic mirror. We have continued to inquire into a means to solve the latter problem. We here propose a new way which will be able to make a magnitude of a loss angle of a magnetic mirror for deuterons virtually zero.


Introduction
It would seem that researches for a magnetic mirror fusion reactor are far behind in comparison with ones for Tokamak. The cause may be that a magnetic mirror field has configuration being open-ended [1] [2]. However, recently, a new magnetic mirror reactor scheme [3] was proposed. The scheme tries to solve the problem of the negative curvature by making a mirror length very long so that the region with the negative curvature may nearly vanish. Also, it uses helical winding coils at both ends of the mirror bottle. The helical windings resemble those in Stellarator and will be stronger than a magnetic field of a solenoid, with respect to the magnetohydrodynamic instability due to gravity or charge-separation. However, the helical windings do not intend to suppress the number of escaping charged particles as much as possible. We previously reported a plan [4] in which a supplemental magnetic mirror (called SMM) is connected to the exit of a magnetic mirror bottle. SMM had the spaces for heating charged particles by cyclotron resonance waves within. The main results are as follows: 1) The magnitude of the loss angle decreased from 14.5˚ (in the exit of the bottle) to about 5˚ (in the exit of SMM) by accelerating velocity components perpendicular to the magnetic field. 2) However, nonrelativistic particles (deuterons) had inherent disadvantage that the acceleration invites deuterons from being outside the loss cone into inside the loss cone. Relativistic particles (electrons) were not related to such an effect. 3) Heavy deuterons required a very long flight length and a very powerful electric field in order for those to get a necessary velocity by the acceleration.
Also, we found a mistake (deuterons are not heated, in a high density plasma, by an extraordinary wave with an ion cyclotron frequency). It may be impossible to make a loss angle for deuterons zero by relying only on acceleration with electric waves. In this work, together with re-consideration of the plasma heating by an extraordinary wave [5] [6] [7], we inquire into a new way of reflecting a deuteron having a very fast velocity by a constant electric field which is not extremely large.

A New Plan to Reclaim Escaping Deuterons
We assume that the most part of the bottle is filled with such an ideal plasma consisting of electrons and deuterons as shown below: ◎ Electron density n e = deuteron density ◎ Plasma temperature The mean thermal velocity υ of electrons 1.2 10 m sec.
A necessary magnetic pressure 2 2 2 N m B µ (where, B is a magnetic field and μ is the permeability of vacuum 4π × 10 −7 mT/A) to stand against p P is given by υ" at time t = 0. D + ion is a nonrelativistic particle.
The velocity y υ of D + ion decreases according to In the flight from plane (a) to plane (c), let us an effective length by which the electric field y E acts on D + ion to be  m.
Since the ratio L ⊥  r is 4.6/0.78 ≃ 6, the most part of deuterons escaping from plane (c) to the solenoid ought not to touch the wall of the solenoid. Even if a part of high-energy deuterons collide with the wall, a sincere problem will not arise if only we make the number of colliding deuterons sufficiently small.

Plasma Heating by Extraordinary Waves (Called X-Waves)
Since we consider that heating of charged particles should be slowly done outside a main bottle so as not to disturb the stability of a plasma within the bottle, we consider heating deuterons in App (A) with X-wave (the frequency r2 ω shown after) and electrons in App (B) with another X-wave (the frequency r1 ω shown after).
The refractive index x n for X-wave with a frequency ω [8] is given by Here, Two resonance frequencies are found from We try concrete numerical calculations on r1 ω and r2 ω .
We assumed just now that a magnetic field strength B in the exit of the main

Discussion and Conclusion
In very slow, we consider that such an effect as mentioned above has hardly influence on the magnitudes of E y and E z . "If the constant electric field E y works well", the apparatus in Figure 1 can make a magnitude of a loss angle for deuterons virtually zero. We consider that a combination of the apparatus in Figure 1 and a long mirror bottle has engineering simplicity.

Conflicts of Interest
The author declares no conflicts of interest regarding the publication of this paper.