Adam Michael Darr

The graphite-differential absorption spectrometer (G-DAS) is a diagnostic sensor being developed to characterize the high-energy x-ray spectrum emitted by pulsed power machines, enhancing our understanding of the radiation environment and source dynamics. Using an inverse model, G-DAS employs a beam transmission analysis technique where the spectrum is unfolded from transmission signals acquired after the photon beam passes through a segmented graphite stack of six attenuating graphite disks, each 4 cm thick. Each gap (2 cm) between disks has two CaF2 thermoluminescence detectors for measuring the deposited energies. Drawing parallels to methods used to specify photon spectra of clinical linacs, the G-DAS analysis assumes that the spectra from pulsed power machines follow a parameterized functional form based on bremsstrahlung physics. Each spectrum can then be fully characterized by a unique set of those parameters, reducing the task to only determining the free parameters for the spectrum in question. The performance of the implemented method is evaluated using experimental and Monte Carlo simulated transmission data as well as synthetic spectra.

Calculating the space-charge-limited-current density (SCLCD) for a complicated diode geometry often requires computationally expensive particle-in-cell (PIC) codes. This paper addresses this issue by using the charge-free electric field E0 calculated using COMSOL Multiphysics to determine local and global SCLCD. The SCLCD obtained by using the surface average of E02 on the cathode recovers theoretical results for one-dimensional (1D) planar, cylindrical, and tip-to-tip geometries in appropriate limits. We next compared tip-to-tip calculations with the SCLCD obtained using the PIC code Empire. The SCLCD calculated using COMSOL agreed well with Empire for flatter 1D tip-to-tip geometries and diverged with increasing sharpness. Physically, Empire predicts lower SCLCD than COMSOL because the electrons spread due to concentrated space-charge at the tip, whereas theory assumes that the electrons follow the charge-free electric field lines. We further assess the behavior of the SCLCD for tips protruding from the centers of flat, circular plates of various areas. Larger plate areas with constant tip size recover the 1D planar SCLCD globally and 1D tip-to-tip SCLCD locally, while reducing the difference between Empire and COMSOL calculations since larger plates capture more of the emitted electrons, reducing SCLCD suppression due to beam spreading. These results show that charge-free electric field simulations can be used to determine the SCLCD without needing to simulate particle dynamics in PIC.

Magnetically insulated transmission lines (MITLs) are critical components for efficiently transporting power from pulsed power sources to a diverse range of loads, including magneto-inertial confinement fusion and radiation production. This study investigates the behavior of planar MITLs, taking into account the source voltage and source and load impedances, using two-dimensional theory and simulations. Self-limited behavior, where the MITL operating impedance (voltage divided by current) is insensitive to the value of load impedance, is extended to small-to-large gap distance MITL transitions. Load-limited behavior, in which the load impedance is below the self-limited impedance, causes the MITL operating impedance to adjust to match the load impedance and can be extended to describe large-to-small transitions. In both cases, the operating impedance of the larger MITL section changes to match the self-limited operating impedance of the smaller section. This behavior extends to multiple transitions and to both low and high impedance loads. Assuming equilibration occurs (pulse duration larger than MITL transit time), the entire MITL operating impedance becomes the self-limited impedance of the smallest-gap MITL section or the load impedance, whichever is lower.

Bijective point transformations were recently used to derive the classical space-charge-limited current (SCLC) in one-dimensional (1D) nonplanar devices for electrons emitted into vacuum with nonzero monoenergetic initial velocity. Using these transformations, we first derive a canonical form of SCLC for a relativistic diode with zero initial velocity that holds for any orthogonal 1D geometry and recovers the previously derived planar result. We extend this result to derive a canonical form of SCLC that accounts for nonzero monoenergetic initial velocity and relativistic effects, while recovering SCLC for nonrelativistic diodes with zero and nonzero initial velocity and the relativistic diode with zero initial velocity in appropriate limits. We then use appropriate bijective point transformations to convert from the canonical solution to concentric cylindrical and spherical coordinates. This equation has no closed form solution and must be numerically integrated. The relativistic effects of initial velocity do not become significant until the Lorentz factor γ0≳1.1; for lower γ0, nonrelativistic SCLC gives a reasonable approximation. In the ultra-relativistic limit, Jr,SCLC/JSCLC∝V1/2, where Jr,SCLC and JSCLC are the SCLC for the relativistic diode with general initial velocity and nonrelativistic diode with zero initial velocity, respectively. These asymptotic equations match the exact solutions for sufficiently large γ0 and V. This analysis provides an exact, numerical solution for SCLC for nonzero monoenergetic initial velocity that incorporates relativistic effects for any 1D orthogonal geometry.

Magnetic insulation of electrons prevents losses and can be applied to generating radiation or electron sources for high current and high power applications. Ion emission from the anode may degrade magnetic insulation. We develop equilibrium theory, self-consistently coupling magnetically insulated electron flow with free-flowing injected ions. Generally, ion injection is self-limiting from space charge; however, once insulation strength drops below about 1.2x the magnetic insulation threshold, ion space-charge limits vanish. The gap effectively short-circuits and the electron flow layer asymptotically approaches the anode. In this regime a quasineutral, nonthermal plasma manifests, effectively reducing gap distance and suggesting quasiequilibrium gap closure evolution.

Theoretically and computationally describing the operation of nanodiodes requires characterizing the transitions between multiple electron emission mechanisms for nanodiodes with complicated geometries. This motivates our development of techniques to determine when simplified theories for individual mechanisms suffice compared to more complete, but more computationally expensive, models. Leveraging recent theories that define a canonical gap distance to translate planar theory to nonplanar diodes, we derive the conditions for the transitions among thermal emission, field emission, and space-charge-limited current density (SCLCD) in vacuum and with collisions for non-Cartesian coordinate systems, including spherical, cylindrical, and prolate spheroidal coordinate systems. Particle-in-cell (PIC) simulations of the current density as a function of applied voltage for a tip-to-plate geometry in vacuum agreed qualitatively with the asymptotes for thermal emission at low voltage and SCLCD at higher voltage using the canonical gap distance. This demonstrates the utility of this approach for guiding system design and suggests future extensions to save simulation time for more realistic geometries that are more computationally expensive.