On the efficacy of imploding plasma liners for magnetized fusion target compression

Abstract

A new theoretical model is formulated to study the idea of merging a spherical array of converging plasma jets to form a “plasma liner” that further converges to compress a magnetized plasma target to fusion conditions [Y. C. F. Thio et al., “Magnetized target fusion in a spheroidal geometry with standoff drivers,” Current Trends in International Fusion Research II, edited by E. Panarella (National Research Council Canada, Ottawa, Canada, 1999)]. For a spherically imploding plasma liner shell with high initial Mach number (M=liner speed/sound speed) the rise in liner density with decreasing radius r goes as ρ∼1∕r2, for any constant adiabatic index γ=dlnp∕dlnρ. Accordingly, spherical convergence amplifies the ram pressure of the liner on target by the factor A∼C2, indicating strong coupling to its radial convergence C=rm∕R, where rm(R)=jet merging radius (compressed target radius), and A=compressed target pressure/initial liner ram pressure. Deuterium-tritium (DT) plasma liners with initial velocity ∼100km∕s and γ=5∕3, need to be hypersonic M∼60 and thus cold in order to realize values of A∼104 necessary for target ignition. For optically thick DT liners, T<2eV, n>1019–1020cm−3, blackbody radiative cooling is appreciable and may counteract compressional heating during the later stages of the implosion. The fluid then behaves as if the adiabatic index were depressed below 5∕3, which in turn means that the same amplification A=1.6×104 can be accomplished with a reduced initial Mach number M≈12.7(γ−0.3)4.86, valid in the range (10<M<60). Analytical calculations indicate that the hydrodynamic efficiency for plasma liners assembled by current and anticipated plasma jets is <4%. A new similarity model for fusion α-particle heating of the collapsed liner indicates that “spark” ignition of the DT liner fuel does not appear to be possible for magnetized fusion targets with typical threshold values of areal density ρR<0.02gcm−2.

One-dimensional radiation-hydrodynamic scaling studies of imploding spherical plasma liners

“…3 displays the temporal evolution of the cell that is initially 1.0 cm from the leading edge of the liner (r 0 =R m +1.0 cm) for case 6 of Table 2 Prior to the leading edge of the liner reaching the origin (from t=0 to t~5 µs), the plasma exhibits quasi-steady-state behavior, with spherical convergence resulting in increased pressure and density. In the liner interior, to high accuracy, the density increases as ρ(r)=ρ 0 (r 0 /r) 2 (r 0 and r are the initial and time varying radius, respectively, of the fluid element), which has been reported earlier for high-M spherically convergent flows [15,16]. Near the liner edges (vacuum interfaces), rarefaction waves initially result in reduced local density and a slightly broadened density profile.…”

Experimental evidence for collisional shock formation via two obliquely merging supersonic plasma jets

“…5,12,49,51 A concern is that jet merging would lead to shock formation and heating that would significantly decrease M (compared to its initial value) and, thus, implosion performance. The results reported here are encouraging in that the experimentally inferred increases in T e [by up to a factor of (2.3 eV)/(1.4 eV) = 1.64] andZ (by up to a factor of 1.4/0.94 = 1.49) lead to an increase in C s ∼ (ZT e ) 1/2 of 56% (we caution that more data is needed to establish a more accurate upper bound on T e in the merged case).…”

“…These physics issues have been considered recently via theory and numerical modeling. 4,49,50 In spherical plasma liner formation via an array of plasma jets, the initial merging would be among more than two jets, and the detailed merging geometry would depend on the port geometry of the vacuum chamber. In the case of PLX, a quasi-spherical arrangement of 60 plasma guns would result in twelve groups of five jets, with each group arranged in a pentagonal pattern.…”

Possible energy gain for a plasma-liner-driven magneto-inertial fusion concept

“…The efficiency of plasma guns creating and launching the jets can be optimized for a given velocity. Several recent studies have investigated various aspect of PJMIF: [11][12][13][14][15][16][17][18][19][20][21]. Methodical experimental efforts were initiated at Los Alamos National Lab (LANL) [22,-24] in collaboration with Hyper V Technologies [10,25], and the University of New Mexico [26].…”