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Astron Thermonuclear Reactor P/2446 USA Astron Thermonuclear Reactor By N. С Christofilos* 1. INTRODUCTION scattering, they have a finite lifetime. Hence in order to maintain the E-layer, a continuous injection of The basic requirements of an ideal scheme of con- electrons from outside is required. fining a plasma at an adequate density and tempera- ture to produce thermonuclear reactions on a large 2. ESTABLISHING THE E-LAYER scale can be summarized as follows: (a) A magnetic field pattern must be established The E-layer is established within a long cylindrical whereby the magnetic lines are closed onto them- vessel (Fig. 1). In this vessel a magnetic field is at selves within a vacuum vessel, before injection of first established by means of external coils. The direc- any plasma within this pattern. In addition, it is tion of this field is substantially parallel to the axis of desired that this pattern of closed magnetic lines be the cylinder but converging at both ends in order to axially symmetric with no field components in the azi- reflect the electrons. It is desirable, mostly for mathe- muthal direction. Thus the drifts resulting from field matical convenience, that the gyration radius of the and pressure gradients are all in the azimuthal electrons, as they move along the E-layer, remain direction. Hence, no plasma loss can result from such constant although their azimuthal momentum varies drifts. Since this field pattern must enclose the current as a function of position. This condition is satisfied if distribution, which creates this pattern, the only way the vector potential of the external field obeys the to establish such currents is through organized motion equation of charged particles. (b) Besides providing a pattern of closed magnetic lines, means must be provided for ionizing neutral gas to establish a plasma and, thereafter, for heating this where k = 1.84/г«, r\ is the desired radius of the E- plasma up to ignition temperature. layer, 2L is the length of the E-layer, Ji(kr) is the We hope to meet the above requirements in the Bessel function of first order and a is a constant Astron reactor by a long cylindrical layer of relativistic determining the ratio between the axial and azi- electrons. This layer of rotating relativistic electrons, muthal momentum of the electrons far from the ends hereafter called E-layer, is the key feature of the of the E-layer. Astron concept. It not only performs the above- The electrons are injected at r = r¿, z = L with mentioned functions but, in addition, its presence is a almost zero axial momentum. However, at the point of necessary condition, as will be shown later, in order to injection the electrons encounter a radial component obtain an equilibrium solution of the plasma in the of the magnetic field. Hence, their azimuthal momen- steady state, such an equilibrium solution satisfying tum changes as they move towards the center plane of hydrodynamic, diffusion and electromagnetic equa- the tank. The ratio of the total momentum, p, to the tions. azimuthal momentum, pd, far from the ends is The relativistic electrons ionize neutral atoms and Pipe = 1 + ajoikrt). (2) thus a plasma can be established as soon as the pat- tern of closed magnetic lines is created. The condition The value of Bo is given by the equation for the latter is that the number of relativistic electrons in the E-layer exceed a certain critical number. Then *®° "~ ~~ZT n i „т (h*, vi ' W the relativistic electrons as they rotate inside the plasma lose energy by Coulomb scattering to the where mo is the rest mass and у is the relativistic mass ratio of the electrons. electrons of the plasma. If this energy transfer, which 2 2 is an energy gain for the plasma, is higher than the The constant a must be selected so that 2pe /p > 1 plasma losses by diffusion or other loss processes, the (far from the ends), otherwise the defocusing action of the end fields, in the radial direction, would lead to temperature of the plasma increases. Since the elec- 1 trons of the E-layer are continuously losing energy by unstable electron orbits. This method of injection provides the electrons always with a considerable axial * University of California Radiation Laboratory, Liver- momentum; this constitutes an axial pressure and more, California. prevents the collapsing of the E-layer, in the axial 279 280 SESSION A-9 P/2446 N. С CHRISTOFILOS 2446.1 ELECTRON 6UN OR ACCELERATOR -Е-LAYER ЛАХЛЛЛЛЛЛЛЛЛЛЛЛ^ УУУ V YVW Figure 1. Astron reactor, schematic direction, from the contractive forces of its own the ionization process have acquired also a kinetic magnetic field. The electrostatic charge of the E-layer energy of a few electron volts. Thus as the ionization is assumed to be neutralized by positive ions. continues and the plasma is being established its Since the injection of the electrons must continue, initial temperature is not zero but a few electron volts. after a steady state is established, in order to maintain However, this temperature further increases as the the E-layer, a technique is required allowing external relativistic electrons lose energy, by Coulomb scatter- injection to a region where the magnetic field is con- ing, to the plasma electrons. stant in time. This is accomplished by a combination The energy loss of relativistic electrons is given by of standing and traveling waves whereby electrons the well-known Bethe formula injected from outside, periodically in short pulses, are 2 y = —4ттг пос1пА, trapped in the trough of a traveling wave, forming a е (5) ring of rotating electrons, and irreversibly injected in where no is the density of the plasma electrons and  the region where the E-layer is to be established. is the ratio of the maximum to minimum interaction Details of this injection method are beyond the scope distance. In Eq. (5) it has been assumed that the of the present general description and will be discussed velocity of the electrons is equal to с Then the energy in a later paper. gain per plasma electron is With each bunch or ring of electrons injected in the E-layer region the charge per unit length of the E- и = (b) layer increases. The rotating charges constitute a cur- rent which creates within the volume enclosed by the where Vo = шос2/е, NQ is the number of electrons per 2 E-layer a magnetic field in a direction opposite to cm length of the layer, a0 = 4тгге In Â, r0 is the the external magnetic field. Thus the net value of plasma radius, the magnetic field within this volume decreases con- 2 Cr° tinuously as the charge of the E-layer increases. When a = —5— nrdr (6a) the number of electrons in the E-layer, per cm length of the layer, reaches a critical value No equal to and no is the plasma electron density near the E- layer; и and Vo are expressed in the same units. No = y ¡re (4) The temperature of the plasma continues to rise as (where re is the classical electron radius), then the long as the rate of losses due to diffusion across the magnetic field inside the volume enclosed by the E- magnetic Hnes and other processes is lower than û. layer far from the ends is reduced to zero. Then the The rate of these losses in comparison with the energy field within the enclosed volume can be reversed by gain will be discussed later in Section 6 of this paper. increasing the charge per unit length of the layer a We observe, however, that the energy gain is pro- little more. At that moment the combination of the portional to the charge per unit length of the layer, external field with the E-layer field provides the which in turn, by Eq. (4), is proportional to the pattern of closed magnetic lines. relativistic mass ratio of the E-layer electrons. 3. INITIAL PLASMA FORMATION 4. PLASMA EQUILIBRIUM As soon as the pattern of closed magnetic lines is As soon as the plasma temperature starts to rise, established, concentration of plasma is possible within the plasma pressure also rises. Since the last closed this pattern. By injecting neutral particles within the magnetic line constitutes the boundary of the plasma, vessel, these particles become ionized as they travel the pressure is zero at this boundary. Hence a pressure through the E-layer region. The electrons liberated by gradient is created across the magnetic lines. Because ASTRON THERMONUCLEAR REACTOR 281 of this pressure gradient, the plasma starts diffusing magnetic field have been computed. The results are outwards, and furthermore a Hall current is created shown in the graphs (Figs. 2 and 3). In Fig. 2 a cross which crossed with В (the magnetic field)balance s the section is shown on a plane through the axis of sym- pressure gradient. This Hall current in turn modifies metry. The magnetic lines (which are also equipressure the pattern of closed magnetic lines. This modification, lines) are shown as well as the shape of the plasma at however, tends to enhance the intensity of the mag- the ends. The line where p = 0 is the last closed netic field; thus the pattern of closed magnetic lines magnetic line. Hence it constitutes the plasma boun- becomes denser as the plasma pressure rises. Of course dary. A line just outside this boundary line is open during the buildup of the plasma pressure the and it goes out along the axis. Two of these Unes are external magnetic field must be increased so that, far shown in Fig.
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