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A Prototype Thick-Target Bremsstrahlung Model with Angularly-Dependent Emission in the MCNP6 ® Code

This document summarizes the current thick-target bremsstrahlung (TTB) model in MCNP and provides test results for an alternative implementation to improve the accuracy with reduced cost compared to full electron transport. It has been observed that the current TTB model produces inaccurate results in problems where the medium is thick with respect to electrons, but the photon distribution in the problem has a strong directionality. An example of such a simulation is detectors surrounding a metal target irradiated with a radiographic beam of high energy photons. The primary cause of this discrepancy is the current TTB method emits all bremsstrahlung photons in the same direction as the primary electron produced from each (γ, e ± ) interaction, leading to artificially forward peaked photon distributions for intermediate to high-energy incident photons. To improve the TTB model, we have implemented an angularly-dependent TTB model in a developer version of the MCNP6 ® code; for developers, this was done on the branch prototype/angular_ttb in the mcnp6 repo on bitbucket. The angularly-dependent TTB model accounts for the energy and scattering of electrons as they slow down in the current material, but does not sample the computationally expensive energy straggling, secondary electron events, and tracking electrons; this approach is significantly less computationally expensive than full electron transport and can be comparable to the original TTB method for problems with sufficiently complex materials and geometry. To evaluate the method, we have modeled a simple problem of a beam of 5 MeV photons incident on a sphere of plutonium surrounded by detectors at different deflection angles. For this problem, the angularly-dependent TTB produces a photon flux within 8.0% for a 90 degree deflection angle and 0.8% along the beam axis, as compared to the electron transport solution. This is an improvement compared to a 43% and 81% discrepancy with the original TTB method, respectively. The rest of this work includes the following: the first section details the current TTB treatment in MCNP, which has not been well documented elsewhere. Then, the modified TTB algorithm is detailed and the approximations compared to the condensed history algorithm are compared. Results are given comparing the two TTB methods to the condensed history transport algorithm. The appendix includes details for code developers on relevant electron transport implementation details and potential code improvements for future work.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

The quasi-linear relaxation of thick-target electron beams in solar flares

The effects of quasi-linear interactions on thick-target electron beams in the solar corona are investigated. Coulomb collisions produce regions of positive gradient in electron distributions which are initially monotonic decreasing functions of energy. In the resulting two-stream instability, energy and momentum are transferred from electrons to Langmuir waves and the region of positive slope in the electron distribution is replaced by a plateau. In the corona, the timescale for this quasi-linear relaxation is very short compared to the collision time. It is therefore possible to model the effects of quasi-linear relaxation by replacing any region of positive slop in the distribution by a plateau at each time step, in such a way as to conserve particle number. The X-ray bremsstrahlung and collisional heating rate produced by a relaxed beam are evaluated. Although the analysis is strictly steady state, it is relevant to the theoretical interpretation of hard X-ray bursts with durations of the order of a few seconds (i.e., the majority of such bursts).

Mcclements, K. G.↗

A comparison of the thick-target model with stereo data on the height structure of solar hard X-ray bursts

The thick target, hard solar X-ray source height structure is predicted for the case of a beam that is injected vertically downward, having a power law spectrum, being dominated by Coulomb collisional energy losses, and being structurally characterized by the ratio of hard X-ray flux from an upper part of the source to that from the entire source. These predictions are compared with the flux ratios at 150 and 350 keV which were observed by two spacecraft for five events in which the solar limb occults part of the source for one spacecraft. The energy dependence of the occultation ratio is found to be inconsistent with that predicted by the model, and it is concluded that noncollisional losses must be significant in beam dynamics.

Brown, J. C.↗

Microwave signature of thick-target electron beams in solar flares

The steady-state behavior of a flux of nonthermal electrons injected into a fully ionized thick target is examined. Owing to the (inverse square) energy dependence of the Coulomb collisional cross section, it is found that injected electron distributions that are monotonically decreasing functions of electron energy develop at finite depths into distributions that have 'humps' in velocity space; the electron energy corresponding to the hump correlates with the overlying particle column density to the target. This results in a two-stream unstable situation. The distribution is constantly being relaxed by quasi-linear relaxation and re-created by collisions; in this way a steady nonthermal level of Langmuir plasma waves is created, and these waves in turn produce microwave plasma radiation with a typical flux of 3 x 10 to the -16th erg/sq cm-sec. This flux can be enhanced by a factor of up to 100 by a high level of low-frequency (such as ion-acoustic) turbulence, which prevents quasi-linear relaxation for a sufficient fraction of the path length.

Emslie, A. G.↗

Picosecond lifetime measurements of resonances using a thick-target invariant-mass technique

Here, a new technique is presented for measuring the half-lives of resonances in the picosecond range using presently available invariant-mass apparatus and a thick target. For short-lived resonances, the energy losses of the decay fragments in the target material change their relative velocities giving rise to a poor invariant-mass resolution. However, for longer-lived resonances that travel through the remaining target material before decaying outside of the target, this dominant contribution to the resolution is eliminated. The measured invariant-mass peak will then display a narrow peak from these events which sits on a wider structure associated with the remaining events that decay in the target. The fraction of the events in the narrow peak is related to the probability that the resonance leaves the target before decaying and hence is related to the lifetime. This technique is exercised for the 2.685-MeV resonance in 33 Cl which decays by emitting an f -wave proton. A half-life of T 1/2 =5.7$^{+4.1}_{-2.5}$ ps was measured which is consistent with values inferred from other known properties of this resonance.

lifetimes & widths↗

Determination of the mean energy of fast electron losses and anisotropies through thick-target emission on WEST

Abstract A new method to obtain the mean energy of fast electron losses in fusion plasmas using a versatile multi-energy hard x-ray (HXR) detector is presented. The method is based on measuring the thick-target emission of tungsten in the divertor region produced by fast electron losses interacting with the target and modeling the tungsten spectra by a Monte Carlo code which simulates the interaction between a beam of electrons and a solid target. The mean energy of the fast electron losses is determined through the comparison between the experimental and synthetic emission. The results show that fast electron losses during lower hybrid current drive discharges at WEST have a mean energy of 90–140 keV and represent only 2% of the total heat flux at the target. Additionally, anisotropic HXR emission has been detected for the first time at the WEST core and edge plasma, with opposite directions. It is due to the forward-peak emission of two distinctive populations of fast electrons: co-current fast electrons in the core and counter-current fast electron losses at the inner strike point. In view of future experiments like ITER where electron cyclotron current drive will generate a fast electron population, this technique could serve as a real-time monitor of fast electron losses and eventually feed an actuator on the current drive generation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Bremsstrahlung spectra from thick-target electron beams with noncollisional energy losses

A generalization of the Brown's (1971) formulation of the relationship between bremsstrahlung spectrum and mean electron spectrum (electrons in the range 10-100 keV) is presented with an objective of demonstrating the information content of bremsstrahlung spectra from a thick target. It is shown that the observed photon spectrum can be inverted to yield an integral functional of the electron spectrum and the effective energy loss rate. Furthermore, if observational or theoretical electron injection spectrum is known, an effective 'phenomenological' energy loss function can be obtained.

Brown, J. C.↗

Gas dynamics in the impulsive phase of solar flares. I Thick-target heating by nonthermal electrons

A numerical investigation is carried out of the gas dynamical response of the solar atmosphere to a flare energy input in the form of precipitating nonthermal electrons. Rather than discussing the origin of these electrons, the spectral and temporal characteristics of the injected flux are inferred through a thick-target model of hard X-ray bremsstrahlung production. It is assumed that the electrons spiral about preexisting magnetic field lines, making it possible for a one-dimensional spatial treatment to be performed. It is also assumed that all electron energy losses are due to Coulomb collisions with ambient particles; that is, return-current ohmic effects and collective plasma processes are neglected. The results are contrasted with earlier work on conductive heating of the flare atmosphere. A local temperature peak is seen at a height of approximately 1500 km above the photosphere. This derives from a spatial maximum in the energy deposition rate from an electron beam. It is noted that such a feature is not present in conductively heated models. The associated localized region of high pressure drives material both upward and downward.

Nagai, F.↗

Preparation of thick molybdenum targets

Thick natural molybdenum deposits on nickel plated copper substrates were prepared by thermal decomposition of molybdenum hexacarbonyl vapors on a heated surface in an inert gas atmosphere. The molybdenum metal atoms are firmly bonded to the substrate atoms, thus providing an excellent thermal contact across the junction. Molybdenum targets thus prepared should be useful for internal bombardment in a cyclotron where thermal energy inputs can exceed 10 kW.

Singh, J. J.↗

Thick target neutron yields from Beryllium, Carbon, Tungsten, and Lead targets irradiated by 26.7 MeV/nucleon 4 H e ions

The angular and energy distributions of secondary neutrons produced from 26.7 MeV/nucleon 4 He ions, stopping in thick Be, C, W and Pb targets are measured by the time of flight method. The GEANT4, PHITS, and FLUKA Monte Carlo simulation codes with different physics models are employed to simulate the neutron yields and the results are compared with the experimental data. For the thick Be and C targets, GEANT4 with INCL++ reproduces the experimental data reasonably well. Whereas PHITS with JQMD-2.0 overestimates the neutron yields at intermediate energies and FLUKA with PEANUT underestimated the neutron yields at intermediate energies. For W and Pb targets, FLUKA with PEANUT physics model agree with experimental data best. PHITS with JQMD-2.0 overestimates the neutron yield at intermediate energies at 0°, and GEANT4 with INCL++ underestimates the neutron yield at intermediate energies at three angles.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗