Schematic of the 2D parallel-plate MITL simulation model (not drawn to scale).
Plots of the magnitudes of the (a) electric and (b) magnetic field profiles and (c) the sheath number density between and 65 cm after 10 ns from the full MITL simulation at 3.22 MV.
(a) Average sheath density, (b) electric field, (c) magnetic field, and (d) current density as a function of distance across the AC gap for three simulations at 1.47, 3.22, and 10.57 MV. All data averaged in between 55 and 65 cm after steady-state equilibrium conditions are reached .
Sample electron orbits in the equilibrium section of the sheath, launched from the cathode at for the 3.22 MV simulation. Test electrons are launched at , 50, 55, 60, and 65 cm.
Schematic of the MITL flow model in the planar diode configuration.
Equilibrium MITL characteristics from the 3.22 MV PIC simulation (solid curves) and the analytic model of Sec. III A (dashed curves representing case 3sim from Table II) plotted as a function position between the cathode and anode . The sheath electron density is plotted in (a) along with the density from the minimum current Brillouin flow theory (dot-dashed curve). The and field components are compared in (b) and (c) and the sheath current density is compared in (d).
(a) Sheath density, , and (b) unstable growth rate spectra for the 3.22 MV model sheath equilibria given in Table II.
Eigenfunctions for the case 3b equilibrium of Table II at (a) , (b) , and (c) .
(a) Sheath density profiles and (b) growth rate spectra for Brillouin flow equilibrium with (dashed curves) and the case 3c equilibrium (solid curves).
Schematic of the 2D idealized PIC simulation geometry. The simulation box is of length with periodic boundaries at and . The anode and cathode are conducting boundaries separated by a distance . A laminar sheared electron sheath profile is preloaded into the simulation along with the initially static magnetic and electric equilibrium fields.
Sample instability growth rate calculation result for case 3b perturbed at . The solid circles are the electric field amplitude associated with the perturbed wavelength at different times. The line indicates the growth rate calculated from the stability model.
Normalized (a) real and (b) imaginary frequencies as a function of dimensionless wavenumber . The black curves are from the dispersion analysis applied to the case 3b sheath density profile. The individual points are from idealized simulations of the case 3b equilibrium perturbed at different wavelengths.
(a) Sheath density and (b) magnetron instability growth rate spectra for equilibria corresponding to Eq. (2) with , , , and and five values of the slope parameter : (Brillouin flow) and .
Values of the high cutoff as a function of the inverse scale length parameter for the equilibria of Fig. 13(a) with .
(a) Sheath density and (b) unstable growth rate spectra for the 1.47 MV model sheath equilibria given in Table II. In (b), no unstable modes were found for case 1sim, the fitted equilibrium PIC simulation profile.
(a) Sheath density and (b) unstable growth rate spectra for the 10.57 MV model sheath equilibria given in Table II. In (b), no unstable modes were found for case 10sim, the fitted equilibrium PIC simulation profile.
Comparison of the sheath number density profiles. The initial sheath profile from case 3b is shown as a thin solid line. After 3.7 ns of simulation time, this profile evolves to the thick solid curve. This sheath profile is consistent with the “stable” sheath profile that arises self-consistently in long-MITL simulations (dashed curve) described in Sec. II.
Measured voltage (dashed line) near the beginning of the transmission line from Ref. 37 and the voltage (solid line) at from the LSP simulation.
Comparison of the measured and simulated anode (solid) and cathode (dashed) currents at five positions along the 10-m-long MITL. The left-hand side of the shaded boxes in frames (a)–(d) indicates the arrival time of the retrapping wave launched when the self-insulated wave front reaches the load in the experiment. The measured waveforms shown here are adapted from Fig. 3 of Ref. 37.
Comparison of the anode , cathode , and electron sheath currents in the PIC simulations with the results of the MCB model. The ratio of the PIC-to-MCB currents is also given.
Fitting parameters for the sheath equilibria used in the 3.22 MV stability analysis. Case 3sim corresponds to the equilibrium sheath profile in the PIC simulation result at 3.22 MV (see Sec. II). Cases 3a–3c are hypothetical sheath profiles as discussed in the text.
Fitting parameters for the sheath equilibria used in the 1.47 and 10.57 MV stability analyses. Cases 1sim and 10sim correspond to the equilibrium sheath profile in the PIC simulation results at 1.47 and 10.57 MV, respectively. Cases 1a–1c and 10a–10c are hypothetical sheath profiles as discussed in the text.
Comparison of the anode , cathode , and electron sheath currents in the PIC simulation with the results of the MCB model for the Di Capua–Pellinen experiment at 1.6 MV. The average peak measured values for the anode and cathode currents are also given.
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