Patent Number: 044252951
Section: description

The selective electron heating described above is accomplished by means of injecting very particular waves which are absorbed by electrons which satisfy the resonance condition .omega.-k.sub..parallel. v.sub..parallel. =n.OMEGA..sub.e, where .omega. is the wave frequency, k.sub..parallel. is the wave parallel wavenumber, v.sub..parallel. is the electron parallel velocity, .OMEGA..sub.e is the electron gyrofrequency and n is an integer. To assure that the electrons resonant with the wave all travel in one parallel direction, a spectrum of waves is chosen that has only one sign of .omega./k.sub..parallel., the wave parallel phase velocity. FIG. 1 shows a top view of the tokamak chamber with two such typical wave excitation structures for providing the requisite waves. Before explaining the positioning of these structures, we remark that in a tokamak, .OMEGA..sub.e is a function of horizontal position, so that as the wave propagates into the tokamak, electrons with different v.sub..parallel. become resonant. In order that the wave heat electrons with only one sign of v.sub..parallel. at all horizontal positions, the wave is launched so that it is substantially absorbed before it reaches the resonant layer, where .omega.=.OMEGA..sub.e. Beyond this layer, which may be visualized in FIG. 1. as the surface of a cylinder whose axis passes through the symmetry point O, the minute residual wave energy could be absorbed by electrons traveling in the wrong direction. There are two leading wave candidates for this type of electron heating, the ordinary wave and the extraordinary wave. The ordinary wave must be launched from the low-field side of the tokamak where .omega.&gt;.OMEGA..sub.e. In FIG. 1, structure 1 is a section of waveguide that is used as a means of exciting the ordinary wave. A horn antenna may optionally be used to couple to this wave in the plasma with electric field E taken substantially in the parallel direction at the waveguide mouth. The extraordinary wave may also be launched by means of a horn antenna, except that the launching must proceed from the high-field side of the tokamak where .omega.&gt;.OMEGA..sub.e and E must be substantially in the vertical direction at the waveguide mouth. In FIG. 1, structure 2 depicts a section of waveguide that is used as a means of exciting the extraordinary wave. The broken lines 3 and 4 in structures 1 and 2 show the waveguide axes and the waves are launched primarily in the direction of the axes. The angles .phi.1 and .phi.2 are chosen different from zero, representing a tilt of the waveguides in the horizontal plane in order to launch the required spectrum of waves that travel in only one toroidal direction. As the extraordinary wave propagates into the plasma, the wave energy is absorbed by the resonant electrons which travel in the toroidal direction opposite to the wave parallel phase velocity. Near the edge of the tokamak, where the magnetic field is highest, the resonant electrons have the largest parallel phase velocity. As the wave propagates inward, electrons with slower parallel phase velocities become resonant. When the wave passes the resonant layer, electrons going in the wrong direction become resonant. Propagation studies by Ott et al. (1980) show that for a variety of tokamak conditions nearly all the wave energy is absorbed before the resonant layer is reached. Similar results are shown by Ott also for the ordinary wave, except that this wave is instead absorbed first by fast electrons traveling in the direction of the wave parallel phase velocity. The process described herein for generating currents is most advantageously employed when additional steps are taken to minimize the power required in launching the waves. For fusion applications, this minimization of the wave power is of utmost importance. As pointed out by Fisch et al. (1980), the current is generated with the least wave power when the speed of the resonant electrons is greatest. The way to accomplish absorption of wave energy by the fastest electrons is to angle the waveguide axis such that the wave propagates vertically through the tokamak rather than horizontally. This can be done for processes employing either the ordinary or extraordinary plasma waves. How this is done is best described with reference to FIG. 2. In this figure, line 7 represents a horizontal cut through the tokamak minor cross-section, which is in the plane of the cross-sectional cut of the tokamak chamber defined in FIG. 1. In FIG. 2 the ray .theta.=0 points to the outside of the tokamak whereas the ray .theta.=180.degree. points to the tokamak center, the symmetry point O of FIG. 1. The structure 5 is a section of waveguide with the axis given by the broken line 6. This waveguide section is to be identified either with structure 1 or structure 2 of FIG. 1, depending upon the value of .theta., which determines whether injection is from the low-field side (-90.degree.&lt;.theta.&lt;90.degree.) or from the high-field side (90.degree.&lt;.theta.&lt;270.degree.). Successful vertical angling is accomplished as follows: In employing the ordinary wave it entails picking .theta. slightly less than 90.degree. (or slightly greater than 270.degree.) with .zeta. about 0.degree.. In employing the extraordinary wave it entails picking .theta. slightly greater than 90.degree. (or slightly less than 270.degree.) with .zeta. about 0.degree.. Calculations of the wave trajectories and the wave damping are easily carried out with precision for the asymmetric wave spectrum of interest here just as, for example, Ott et al. (1980) calculated the propagation and damping for symmetric spectrums. A typical example of a successful configuration for current generation would be to pick the angles as follows: in employing the extraordinary wave pick .phi.2=45.degree., .theta.= 105.degree. and .zeta.=0.degree.; in employing the ordinary wave pick .phi.1=45.degree., .theta.=85.degree. and .zeta.=0.degree.. The above described apparatus may be employed to generate current in any toroidal plasma. The foremost application, however, is likely to be for generating current in tokamak devices. These devices are described by, for example, Furth (1975) and the Coppi et al patent. The art relating to the minor changes in the electronic circuitry necessitated by introducing currents other than ohmically generated currents is described by Fisch (1978b). The invention described herein may be useful for providing part or all of the necessary current for confinement of the plasma in tokamaks, particularly those tokamaks which are fusion devices, which confine a mixture of fusionable elements at high temperature. The fusion device may be a producer of net power or merely a copious emitter of high energy neutrons or charged particles. In the latter instance, the high energy neutrons may be useful in subsequent nuclear reactions, for example, as in the so-called fusion-fission hybrid reactor. In the former instance, assuming the fusionable material comprises equal densities of deuterium and tritium ions, then sufficient current for continuous confinement of the plasma requires continuous power dissipated in the plasma, P.sub.d, such that ##EQU1## where P.sub.f is the fusion power generated, n.sub.14 is the electron density normalized to 10.sup.14 cm.sup.-3, T.sub.10 is the temperature normalized to 10 KeV, a.sub.1 and R.sub.1 are, respectively, the minor and major radii in meters, and u and w are, respectively, the resonant electron speed and parallel velocity normalized to an electron thermal speed. The range of applicability of this formula is for 1&lt;T.sub.10 &lt;3. With suitable angling of the waveguides in the vertical direction and for dense large plasmas such as are envisioned for fusion reactors, it is estimated that uw of 20-30 is easily achievable under extraordinary wave injection and somewhat lower but comparable uw is achievable under ordinary wave injection. Thus, the ratio P.sub.d /P.sub.f may be substantially smaller than unity, implying that the apparatus described herein represents an economically attractive means of supplying steady-state current for confinement in a fusion reactor. The formula for P.sub.d /P.sub.f is a useful aid in designing such a reactor in that the recycled power is directly described as a function of macroscopic plasma parameters. Whether the extraordinary or ordinary plasma wave is to be preferred as a means of current generation depends upon technological considerations and preferences. For tokamak fusion applications the ordinary wave has the geometrical advantage of injection from the low-field side of the tokamak, which is less cluttered than the inside of the tokamak. On the other hand, the extraordinary wave is damped more quickly, which enables it to transfer its energy to more energetic electrons, so that the current is generated more efficiently. Also the extraordinary wave utilizes sources with somewhat lower frequency. At the present state of the art, sources with the lower frequency are more efficient. It should be recognized that current generation by selective electron heating in the manner described herein is significantly different from all previously proposed methods of generating currents. This is the only method that both utilizes high frequency sources, wherein .omega. is on the order of .OMEGA..sub.e, and is capable of generating current on the magnetic axis in a tokamak. The advantage of utilizing these waves lies primarily in their high power density, their high coupling efficiency, and their ability to exchange energy with arbitrarily fast electrons. A summary and comparison of all the methods proposed for generating currents is provided by Fisch (1980). Further modifications of the invention herein disclosed will occur to persons skilled in the art and all such modifications are deemed to be within the spirit and scope of the invention as defined by the appended claims.