Time-dependent, x-ray spectral unfolds and brightness temperatures for intense Li+ ion beam-driven hohlraums

Abstract

X-ray-producing hohlraums are being studied as indirect drives for inertial confinement fusion targets. In a 1994 target series on the PBFAII accelerator, cylindrical hohlraum targets were heated by an intense Li+ ion beam and viewed by an array of 13 time-resolved, filtered x-ray detectors (XRDs). The unfold operator (UFO) code and its suite of auxiliary functions were used extensively in obtaining time-resolved x-ray spectra and radiation temperatures from this diagnostic. The UFO was also used to obtain fitted response functions from calibration data, to simulate data from blackbody x-ray spectra of interest, to determine the suitability of various unfolding parameters (e.g., energy domain, energy partition, smoothing conditions, and basis functions), to interpolate the XRD signal traces, and to unfold experimental data. The simulation capabilities of the code were useful in understanding an anomalous feature in the unfolded spectra at low photon energies (⩽100 eV). Uncertainties in the differential and energy-integrated unfolded spectra were estimated from uncertainties in the data. The time–history of the radiation temperature agreed well with independent calculations of the wall temperature in the hohlraum.

Analytic models of high-temperature hohlraums

“…10 and 19 are equivalent; however, Eq. 19 gives T,(t) as a function of f~, fW, T~, and TW, quantities that can be directly measured as a function of time in a hohlraum experiment [83,[87][88][89][90][91][92][93][94][95][96][97][98][99][100][101][102][103][104][105][106].…”

Characterization and error analysis of anN×Nunfolding procedure applied to filtered, photoelectric x-ray detector arrays. I. Formulation and testing

“…For example, a set of orthogonal polynomials defined on ½ÁE or even a sequence of Planckian functions [Eq. (7)] with prescribed temperatures may qualify [14,49]. Knauer [119] and others [103,120] have successfully used higher-order B-splines for filtered-detector arrays.…”

“…III E). The absence or presence of linear dependence thus suggests whether an exact solution or a solution based on some other criteria (e.g., least squares [14,49]) is appropriate.…”

“…The algorithm is, in fact, semiclassical (an N Â N, directly inverted, product-moment method with a priori constraints, histogram basis functions, and collocated data [49,53,54]) and can be implemented on a real-time basis. Previous publications [14,29,[55][56][57] have sketched this algorithm, but no justification or detailed testing of the µ µ µ µ µ µ FIG. 2.…”

“…Particularly tantalizing are hot, optically dense plasmas, in which radiation transport may be studied close at hand and which may approach stellar conditions [5][6][7][8][9]. Such plasmas have been produced on short time scales (& 10 ns) by intense, focused laser beams [10][11][12], particle beams [13,14], and most recently by z pinches of tungsten-wire arrays [15][16][17][18]. Besides their intrinsic interest to physics, these plasmas also emit copious amounts of soft x rays ( $ 50 eV-3 keV), finding application as sources for opacity measurements [9], drivers for inertial confinement fusion (ICF) [19][20][21][22][23], vulnerability testing of materials [24,25], and equation-of-state research [26,27].…”