Dynamics of the super pinch electron beam and fusion energy perspective

The characterization of a high current, relativistic electron beam, designated the Super Pinch electron beam, has been performed using compact pulsed-power accelerators of various architectures with a novel diode geometry. The Thunderbird accelerator has an initial $1.5\text{−}\mu \mathrm{s}$ rise time and 150-kA peak current. The drive voltage is compressed to produce a 12-ns 500-kV voltage pulse generating a $\sim 40\text{−}\mathrm{kA}$ electron beam, which apparently exceeds the Alvén current limit although the useful current at small radius is an order of magnitude less. Using an insulated hollow cathode with a 0.5-cm anode-cathode gap, the large current is enabled by the evolution of plasma from the dielectric sleeve enveloping the cathode and a 0.5-mm wire anode. Post-shot recovery of the anode target and measurements of its deformation and damage allow an evaluation of the enhanced electron-beam focusing whereby significant beam energy is delivered to the record small, microscopic volume inside the anode target. The electron beam is seen to have conditions favorable to those needed to ignite compressed fuel in inertial confinement fusion. These results motivated a deeper insight using theoretical modeling with hybrid particle-in-cell codes. The modeling presented in this paper shows an electron beam radius of $<10\mu \mathrm{m}$ containing a current of 3–6 kA or $>500\mathrm{MA}/{\mathrm{cm}}^2$ current density. Scaling up the accelerator, such preferred focusing, target penetration, and affordability of the pulsed power generated electron beams open a new opportunity for the application of the mainstream pulsed power devices in the research and development of fusion energy.

Figure 1

A picture (left) and schematic (right) of the Thunderbird electron beam accelerator.

Figure 2

Three phases of evolution of the Super Pinch Diode are shown: (1) explosive cathode emission, flashover of the plastic cathode sleeve, plasma formation with high impedance $>20\mathrm{\Omega }$ (top plot); (2) shrinking electrical gap from plasma motion with moderate impedance $5–20\mathrm{\Omega }$ and small beam spot (middle plot); and rapidly falling impedance and plasma envelopes the anode (bottom plot). An electron beam and counter-flowing ion beam are produced across the sheath near the anode. Lower impedance operation occurs as the sheath gap shrinks due to plasma motion and more of the anode is covered by cathode plasma.

Figure 3

The details of the Thunderbird circuit attached to the SPD at the top. The plasma generator (PG) supplies the plasma inventory to the POS.

Figure 4

In (a), the voltage used in the theory and the simulated diode voltage are plotted, in (b) the theoretical and simulated (sim 1 using only thermal desorption of contaminants) diode currents are plotted. Sim1 assumed an $8\times {10}^{15}{\mathrm{cm}}^{-2}$ contaminant areal density.

Figure 5

The computational model of the Thunderbird SPD is shown. The voltage inlet is driven by the Thunderbird circuit. The diode region details are shown in the exploded view. The cathode and anode rod are copper.

Figure 6

The electron densities, on the left, after 5 ns, 10 ns, 15 ns, and 18 ns are plotted for sim1. The enclosed current (or current within the given radius) is plotted on the right.

Figure 7

The diode impedance for the Thunderbird SPD is plotted for various vacuum pressures. (a) the theoretical and simulated (sim1 using only thermal desorption and sim2 with only stimulation desorption of contaminants) diode impedances are plotted, and (b), the simulated (sim1 with $8\times {10}^{15}{\mathrm{cm}}^{-2}$ contaminants and sim3 with $16\times {10}^{15}\text{−}{\mathrm{cm}}^{-2}$ contaminants and sim4 with $4\times {10}^{15}{\mathrm{cm}}^{-2}$ with thermal desorption) diode impedance are plotted.

Figure 8

The experimental current for Thunderbird shot 523 is compared with the simulated diode current (sim1). The X-ray flux is also plotted from two PIN diodes near the diode.

Figure 9

The injected beam current vs time (above) and maximum position of the Cu melt (below) are plotted for the three hole-boring simulations with peak currents of 1.5 kA, 3.0 kA, and 6.0 kA.

Figure 10

A Cu wire is shown from the top (a) and bisected (b) after the Thunderbird shot. A hole has penetrated the wire up to 1 mm with $>0.5\mathrm{mm}$ being blown out. The width of the hole is order 0.1 mm.

Figure 11

The electron (top) and Cu (bottom) densities are plotted for the anode wire in the SPD after 14 ns for the 3-kA peak simulation.

Figure 12

The ignition efficiency of the electron beam energy absorption as a function of fuel density in the heated region at two values of electron beam power $P_b$. The calculated plasma temperature $T$, fusion burn time $t_{\sigma }$, and the power flux of high energy alpha-particles $P_{\alpha }$, normalized by the electron beam power, produced in the heated fuel region are plotted. Minimal value of normalized alpha-particle power flux $P_{\alpha \min }$ required to ignite the adjacent radial layer of fusion fuel (secondary ignition) is given for reference.