S. Krupakar Murali

Space Charge-Limited Flow

chapter 2 discussed solutions to Poisson’s equation for the case of very high currents in spherical geometry. The emphasis was on the buildup of a large space charge of either ions or electrons in the center of the device followed by the formation of one or more virtual electrodes. This then creates a trap for ions which could lead to very large fusion rates. The formation of this trap requires a very high vacuum to avoid ion–neutral fusion reactions or charge exchange with neutrals. This then requires external generation of ions with differential pumping to prevent inflow of neutral gas from the source region. However, as stated in Chap. 2, current experimental devices aimed at near-term applications such as neutron sources do not meet these conditions. Still, quite high currents can be created in these devices. Then their operation, particularly the radial profile for neutron production, requires the use of classical space charge-limited flow analysis, i.e., does not involve formation of multiple virtual electrodes or the so-called double potential well. However, some experiments with gridded IECs that have examined space charge-limited flow show the practical consequences involved in the formation of the converged high-density core plasma.

Background, Basics, and Some IEC Experiments

This book is dedicated to the field of inertial electrostatic confinement (IEC) fusion. Confinement of a hot plasma for fusion or plasma processing is difficult because the hot plasma prevents use of a material confinement vessel. IEC fusion is one of the various methods that can be used to confine a hot fusion plasma. As will be apparent from this book, IEC fusion offers many potential advantages, including simplified support structures and the ability to create non-Maxwellian plasmas that can be used with a variety of fusion fuels. However, a majority of fusion scientists are studying magnetic field confinement in the form of a closed torus (e.g., a Tokamak). Alternately, the fast pulsed approach used in laser fusion attempts to rapidly compress the plasma to an ultrahigh density, and the inertia of the ions maintains the high density long enough such that the fusion energy produced exceeds the input compression energy. Thus, this approach was termed inertial confinement fusion (ICF). These two approaches have led to current major fusion experiments: the international ITER Tokamak in France and the National Ignition Fusion (NIF) experiment using a laser at the Lawrence Livermore National Laboratory (LLNL). Both confinement approaches require very large and complex units, costing billions of dollars to construct. A number of alternate confinement concepts have been proposed with the objective of achieving smaller, less expensive power plants. Some also have the objective of burning “advanced fuels,” defined loosely as any non-D–T fuels [1]. Examples include deuterium–deuterium (D–D), deuterium–helium-3 (D–3He), and hyrdrogen–boron-11 (H–B11). One objective of using such fuels is to minimize neutron production, thus neutron-induced radioactivity and damage in structural materials. A second objective is to reduce or eliminate the need for tritium handling and breeding, greatly simplifying the chamber blanket systems. Hydrogen–boron-11 (or H–B11, often termed p–B11) is ideal with a plentiful fuel supply and a reaction that produces three energetic alpha particles with no neutron (hence aneutronic). However, burning p–B11 generally requires very high ion temperatures (~ 170 keV vs. ~ 25 keV for D–T) and low electron temperatures (< 1/5 the ion temperature), plus elimination of magnetic fields within the hot fusing plasma to minimize Bremsstrahlung and cyclotron radiation losses, respectively. The IEC is one of only a few alternate confinement approaches that theoretically offer the highly non-Maxwellian plasma conditions needed to burn p–B11. Experimental demonstration of this is a key objective for IEC experiments but is very challenging, as discussed in later chapters.

Ion and Electron Current Scaling Issues

Studies to scale an IEC device for higher neutron yields or breakeven fusion operation require the prediction of scaling laws that relate the device performance to the ion and electron current. Ion currents contribute to the fusion reaction rate, while a major energy loss channel occurs through electron currents. Early studies focused on ion beam reactions in the compressed central core region. However, due to high background pressures and modest ion currents in early experiments, it soon became apparent that ion beam–background neutral interactions along with charge exchange reactions and ion interactions with absorbed gas on grid wires were dominant factors. These interactions produce nonlinearities that make the development of scaling laws for internal ion source IECs much more complicated than originally recognized. In addition, breakeven calculations for fusion power concepts involve low-pressure potential well physics, so completely different scaling laws come in.Some approximate reaction rate scaling laws based on the ion density, n 1, in the ion beams illustrate how these conditions radically affect operation. Assuming a deuterium gas filling of the IEC, the volumetric reaction rate, r 1,2 (units of m−3 s−1), arising from monoenergetic populations 1 and 2 of colliding deuterons is given by

Cylindrical and Other IEC Geometries

{r}_{1,2}={n}_1{n}_2\sigma \left({v}_{12}\right){v}_{12},

Effect of Grid Geometry on IEC Performance

where n 1 and n 2 are the respective population densities and v 12 is the magnitude of the collision velocity in the rest frame of either particle (assuming head-on collisions). The subscripts 1 and 2 may refer to either beam deuterons, gas molecules, or those embedded in a solid target. For a fixed grid voltage, we expect the density of beam deuterons to be proportional to the grid current I grid. Thus for beam–beam reactions, we expect to observe

Reactor Confinement Theory and IEC Reactor Visions

{r}_{1,2}\propto {I}_{grid}^2,