
内容記述 
The concept of a fieldreversed configuration (FRC) is attractive for fusion plasmas be<br>cause the magnetic configuration is very simple and a high beta plasma is confined inside the magnetic separatrix. The physics of FRC's has so far been studied from both theoretical and experimental points of view. An ideal MHD theory predicts that compact tori become unstable against an internal tilt mode. On the other hand, many experimental observations show that FRC plasmas remain stable for many growth times. <br> Until now, theoretical and numerical studies have examined various physical effects<br>which have not been taken into account in an ideal MHD theory. They are roughly<br>classified into the following three effects: (A) the finite iota Larrnor radius effect, (B) the profile control effect, and (C) the ton beam effect. However, this contradiction remains<br>unsolved up to the present. For example, the kinetic simulations with the particle orbit<br>effect have disclosed that the tilt mode can be stabilized for a kinetic plasma of <span style=quot;textdecoration:overline;>s</span> ～1,(<span style=quot;textdecoration:overline;>s</span><br>:the dimensionless parameter associated with the ion Larmor radius), but it tends to beunstable for a moderately kinetic plasma of 2 ≤ <span style=quot;textdecoration:overline;>s</span> ≤ 5. On the other hand, in experiments, it is reported that the tilt mode is stable over a wide range of <span style=quot;textdecoration:overline;>s</span> (1<<span style=quot;textdecoration:overline;>s</span> ＜8). This fact means that the tilt stability is not determined only by a single parameter s. The numerical simulation by using an extended MHD model with Hall terms was carried out to verify the profile control effect and found that a FRC with a hollow current profile becomes stable for a high enough separatrix beta value. In this model, however, <span style=quot;textdecoration:overline;>s</span> decreases as the current profile becomes hollow and the stable configuration is realized in kinetic plasmas of <span style=quot;textdecoration:overline;>s</span> ～1. Therefore, this model cannot distinguish the profile control effect from the finite ion Larmor radius effect. In considering which of various effects is a key process leading to the tilt stabilization of FRC plasmas, it is important to develop the physical model which can control each effect independently and deal with them simultaneously. We carry out the threedimensional macroscale electromagnetic particle simulation based on such a physical model. <br> We consider a FRC plasma confined by a uniform external magnetic field within a<br>cylindrical conducting vessel. The plasma consists of thermal ions, thermal electrons, <br>and cold beam ions which are treated as superparticles. The simulation starts front two<br>dimensional equilibrium. The temporal evolution of the system is given by solving both<br>the equations of motion and the Maxwell equations in a selfconsistent manner. In the<br>present model, three kinds of parameters can be controlled independently. The first is the kinetic parameter <span style=quot;textdecoration:overline;>s</span> which controls the finite ion Larmor radius effect. The second are the profile control parameters <i>βsp</i> and D which determine the pressure at the, and<br>the hollowness of the current profile, respectively. The third are the number ratio of the<br>beam ions to the thermal ions <i>Nb/Ni</i>, and the current ratio of the beam ions to the thermal plasma <i>I<small>b</small>/I<small>p</small></i>, which control the ion beam effect. We carry out several simulation runs for a moderately kinetic plasma of 2 ≤ <span style=quot;textdecoration:overline;>s</span> ≤ 5 to clarify the tilt stabilization mechanism<br>in this region. In the first place, we examine the dependences of tilt instability on both<br>the finite ion Larmor radius effect and the profile control effect by carrying out several<br>simulation runs with different values of <i>βsp</i>, <span style=quot;textdecoration:overline;>s</span>, and D. The result is that it is effective<br>against the tilt instability to increase the separatrix beta value (<i>βsp</i>) and the tilt mode<br>can be stabilized for a high <i>βsp</i> (≥ 0.2). On the other hand, the stabilization of tilt<br>mode can be scarcely altered by changing the <span style=quot;textdecoration:overline;>s</span> value and the current profile for low <i>βsp</i><br>( ≤ 0.1 ) and moderately kinetic plasmas. The detailed analysis reveals that the number<br>flux of the ions crossing the magnetic separatrix repeatedly (" cycling ions ") increases in<br>proportion to <i>βsp</i> and the tilt stability is realized for a large number flux of cycling ions. <br> The stabilization mechanism by cycling ions is as follows. Tilt instability is triggered by the internal mode, i.e., the collective motion of plasma is generated inside the magnetic separatrix. The typical cycling ions execute a gradient<i><b>B</i></b> drift in the vicinity of the<br>separatrix, and so they exist outside the separatrix as long as they do inside the separatrix on the average. The ions which make a cyclic motion across the separatrix are not able to follow the collective motion when they are moving outside the separatrix. The phase difference between the collective motions of cycling ions and noncycling ions is created in proportion to the period during which cycling ions exist outside the separatrix. When cycling ions come back inside the separatrix, the internal tilting motion is disturbed by the motion of cycling ions. In other words, they play a role to suppress the tilting motion because their motion is out of phase with the tilting motion. The number of cycling ions increase as <i>βsp</i> increase and thus the tilt mode is stabilized for a high<i>βsp</i>. One can speculate that the cycling ions executing a gradient<b><i>B</b></i> drift play a role as " chain " to connect the internal plasma with the external plasma and stabilize the tilting motion through their " chain " effect. <br> In the second place, we examine the dependences of tilt instability on the ion beam <br>effect by carrying out two types of simulation runs. The first type is the case when the<br>beam velocity varies while keeping the total number of beam ions for each run. The<br>second type is the case when the total number of beam ion varies while keeping the beam velocity for each run. For both cases, the growth rate remains almost unchanged until the current ratio <i>I<small>b</small>/I<small>p</small></i> reaches the critical value of 0.03. However, the growth rate gradually decreases as the ratio exceeds the critical value. The detailed examination reveals that this phenomena can be explained in terms of the effective <span style=quot;textdecoration:overline;>s</span> value, <span style=quot;textdecoration:overline;>s</span> <small>eff</small>, which is obtained by using the average velocity of all ions in place of the ion thermal velocity. The <span style=quot;textdecoration:overline;>s</span> <small>eff</small> value is almost the same as <span style=quot;textdecoration:overline;>s</span> when I<small>b</small>/I</small>p</small> < 0.03. However, the derivation of<span style=quot;textdecoration:overline;>s</span> <small>eff</small> from <span style=quot;textdecoration:overline;>s</span> becomes distinct for I<small>b</small>/I<small>p</small> ＞ 0.03 and <span style=quot;textdecoration:overline;>s</span> <small>eff</small> becomes smaller as I<small>b</small>/I<small>p</small> increases. We have the relation <span style=quot;textdecoration:overline;>s</span> <small>eff</small> ～1 for I<small>b</small>/I<small>p</small> ～ 0.5. It is concluded that the tilt stabilization by the energetic ion beam is realized for the small value of <span style=quot;textdecoration:overline;>s</span> <small>eff</small>. By comparing the above two cases, we examine the relation between the tilt growth rate and the kinetic energy ratio of total beam ions to total thermal plasma. In the case the velocity of beam ions varies, the ion beam needs 40% of the kinetic energy of thermal ions to reduce the growth rate below a half of that for the case without beam ions. On the other hand, in the case the total number of beam ions varies, only 10% of the kinetic energy of thermal ions is needed for the beam ions to get the same growth rate. Thus, the tilt mode can be suppressed more effectively by increasing the number ratio <i>N<small>b</small>/N<small>i</small></i>.<br> 