Control of Deuteron Ions to Escape from the Magnetic Mirror Bottle by a Perpendicular Supplemental Mirror

We have inquired into a means to decrease the number of charged particles escaping from a loss cone of a magnetic mirror reactor as many as possible. We previously reported the way of installing a supplemental magnetic mirror (which has a cyclotron heating space within) at the exit of a main magnetic bottle. The cyclotron heating space was set to increase a reflection-efficiency of the supplemental mirror. We could not suppress the loss of the escaping deuteron ions sufficiently even with a very long mirror and a very powerful electric field. Then, in this work we propose a new plan of installing another supplemental mirror besides the previous supplemental mirror. A new mirror is set perpendicularly to the center axis of the main bottle. By the addition of the perpendicular mirror, an efficiency of sending back of escaping deuteron ions is considerably theoretically improved. Also in the previous work, since we did not touch how to supply a high-frequency electric field to the cyclotron heating space, here we consider supplying it by an extraordinary-wave with a cyclotron frequency. It is mentioned that propagation of an extraordinary-wave with an electron cyclotron frequency depends on a magnetic field strength and density of escaping electrons.


Introduction
It is considered that the most sincere problem in research with respect to a fusion reactor of magnetic mirror-type is that escaping loss of charged particles from the loss cone is still too much [1]. We first examined a means [2] of setting Journal of Modern Physics a supplemental magnetic mirror (with a cyclotron resonance space within) at the exit of a main magnetic bottle. The principal aim in Ref. [2] was to reduce the half-vertical angle (called the loss angle) of the loss cone by the cyclotron resonance heating [3]. However, we could not sufficiently suppress the loss of escaping deuteron ions even with a very powerful electric field and a very long magnetic mirror. So, we proposed introduction of a means for replenishing a large quantity of deuteron ions from the outside. But in this work, we mention an idea that, by setting another supplemental magnetic mirror (called Perp-mirror) perpendicularly to the center line of the supplemental mirror (called Para-mirror) which is set in parallel with the center line of the main bottle, we may be able to induce "most of charged particles escaping from the exit (plane Figure 1) of Para-mirror" outside the loss cone of Perp-mirror. Based on this idea, we mention in §3 a new plan to reclaim escaping charged particles themselves.
We did not touch in Ref. [2] how to supply a high frequency electric field to the cyclotron resonance heating space. Then, in this work we consider transmitting an extraordinary wave with an electron cyclotron frequency or with a cyclotron frequency for a deuteron ion D + to a heating space. It is mentioned in §2 that propagation of an extraordinary wave with an electron cyclotron frequency depends on plasma density and magnetic field strength.

Heating by an Extraordinary Wave
The refractive index x n [4] [5] [6] [7] for an extraordinary wave (called X-wave) with a frequency ω is given by  We examine whether two kinds of X-wave with frequencies c ω and i ω can pass through a plasma.

About X-Wave with ω = ωc
Since 1 e β = and When a value of B is set, an upper limit of e n is determined from (2). We Since it is presumed that a target density for electron density in a main bottle is 21 3 10 m − , we have set an electron heating space behind mirror (b)-(c).

About X-Wave with ω = ωi
We set a heating space for deuteron ions D + between planes (a)-(b). Since There is no essential restriction for values of 2 α and e β .

Sending Back of Escaping Deuteron Ions by a Perpendicular Mirror
Even if Para-mirror of such a large scale as shown in Figure 1 is used, it is clear, based on the examination in Ref. [2], that the escaping loss of charged particles is still too large. Then, we propose a means of installing another magnetic mirror (Perp-mirror) perpendicularly to the center line of the Para-mirror, as shown in  In this plan, the troublesome problem is that a necessary magnitude for 1 E and a necessary length for

Conclusions
We have mentioned the means for sending back most of escaping charged particles to the main bottle by the help of Para-mirror ( Figure 1) and Perp-mirror ( Figure 2). An efficiency of sending back depends on whether charged particles escaping from plane 1 0 4 d d d can pass through plane 2 3 b b or not. As a simple countermeasure, it is considered to make

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