Stanley Humphries

The MICHELLE three-dimensional electron gun and collector modeling tool: theory and design

The development of a new three-dimensional electron gun and collector design tool is reported. This new simulation code has been designed to address the shortcomings of current beam optics simulation and modeling tools used for vacuum electron devices, ion sources, and charged-particle transport. The design tool specifically targets problem classes including gridded-guns, sheet-beam guns, multibeam devices, and anisotropic collectors, with a focus on improved physics models. The code includes both structured and unstructured grid systems for meshing flexibility. A new method for accurate particle tracking through the mesh is discussed. In the area of particle emission, new models for thermionic beam representation are included that support primary emission and secondary emission. Also discussed are new methods for temperature-limited and space-charge-limited (Childs law) emission, including the Longo-Vaughn formulation. A new secondary emission model is presented that captures true secondaries and the full range rediffused electrons. A description of the MICHELLE code is presented.

Computer modeling of the effect of perfusion on heating patterns in radiofrequency tumor ablation

Purpose: To use an established computer simulation model of radiofrequency (RF) ablation to further characterize the effect of varied perfusion on RF heating for commonly used RF durations and electrode types, and different tumor sizes. Methods: Computer simulation of RF heating using 2-D and 3-D finite element analysis (Etherm) was performed. Simulated RF application was systematically modeled on clinically relevant application parameters for a range of inner tumor perfusion (0–5 kg/m3-s) and outer normal surrounding tissue perfusion (0–5 kg/m3-s) for internally cooled 3-cm single and 2.5-cm cluster electrodes over a range of tumor diameters (2–5 cm), and RF application times (5–60 min; n = 4618 simulations). Tissue heating patterns and the time required to heat the entire tumor ± a 5-mm margin to >50°C were assessed. Three-dimensional surface response contours were generated, and linear and higher order curve-fitting was performed. Results: For both electrodes, increasing overall tissue perfusion exponentially decreased the overall distance of the 50°C isotherm (R2 = 0.94). Simultaneously, increasing overall perfusion exponentially decreased the time required to achieve thermal equilibrium (R2 = 0.94). Furthermore, the relative effect of inner and outer perfusion varied with increasing tumor size. For smaller tumors (2 cm diameter, 3-cm single; 2–3 cm diameter, cluster), the ability and time to achieve tumor ablation was largely determined by the outer tissue perfusion value. However, for larger tumors (4–5 cm diameter single; 5 cm diameter cluster), inner tumor perfusion had the predominant effect. Conclusion: Computer modeling demonstrates that perfusion reduces both RF coagulation and the time to achieve thermal equilibrium. These results further show the importance of considering not only tumor perfusion, but also size (in addition to background tissue perfusion) when attempting to predict the effect of perfusion on RF heating and ablation times.

Computer modeling of the combined effects of perfusion, electrical conductivity, and thermal conductivity on tissue heating patterns in radiofrequency tumor ablation

Purpose. To use an established computer simulation model of radiofrequency (RF) ablation to characterize the combined effects of varying perfusion, and electrical and thermal conductivity on RF heating. Methods. Two-compartment computer simulation of RF heating using 2-D and 3-D finite element analysis (ETherm) was performed in three phases (n = 88 matrices, 144 data points each). In each phase, RF application was systematically modeled on a clinically relevant template of application parameters (i.e., varying tumor and surrounding tissue perfusion: 0–5 kg/m3-s) for internally cooled 3 cm single and 2.5 cm cluster electrodes for tumor diameters ranging from 2–5 cm, and RF application times (6–20 min). In the first phase, outer thermal conductivity was changed to reflect three common clinical scenarios: soft tissue, fat, and ascites (0.5, 0.23, and 0.7 W/m-°C, respectively). In the second phase, electrical conductivity was changed to reflect different tumor electrical conductivities (0.5 and 4.0 S/m, representing soft tissue and adjuvant saline injection, respectively) and background electrical conductivity representing soft tissue, lung, and kidney (0.5, 0.1, and 3.3 S/m, respectively). In the third phase, the best and worst combinations of electrical and thermal conductivity characteristics were modeled in combination. Tissue heating patterns and the time required to heat the entire tumor ±a 5 mm margin to >50°C were assessed. Results. Increasing background tissue thermal conductivity increases the time required to achieve a 50°C isotherm for all tumor sizes and electrode types, but enabled ablation of a given tumor size at higher tissue perfusions. An inner thermal conductivity equivalent to soft tissue (0.5 W/m-°C) surrounded by fat (0.23 W/m-°C) permitted the greatest degree of tumor heating in the shortest time, while soft tissue surrounded by ascites (0.7 W/m-°C) took longer to achieve the 50°C isotherm, and complete ablation could not be achieved at higher inner/outer perfusions (>4 kg/m3-s). For varied electrical conductivities in the setting of varied perfusion, greatest RF heating occurred for inner electrical conductivities simulating injection of saline around the electrode with an outer electrical conductivity of soft tissue, and the least amount of heating occurring while simulating renal cell carcinoma in normal kidney. Characterization of these scenarios demonstrated the role of electrical and thermal conductivity interactions, with the greatest differences in effect seen in the 3–4 cm tumor range, as almost all 2 cm tumors and almost no 5 cm tumors could be treated. Conclusion. Optimal combinations of thermal and electrical conductivity can partially negate the effect of perfusion. For clinically relevant tumor sizes, thermal and electrical conductivity impact which tumors can be successfully ablated even in the setting of almost non-existent perfusion.

Grid‐controlled extraction of pulsed ion beams

Experimental results are presented on a method for extracting well‐focused ion beams from plasma sources with time‐varying properties. An electrostatic grid was used to stop the flow of plasma electrons so that only ions entered the extraction gap. In this case, ion flow in the gap was controlled by space‐charge effects as it would be with a thermionic ion source. Constant extracted current was observed even with large variations of source flux. An insulator spark source and a metal‐vapor vacuum arc were used to generate pulsed ion beams. With a hydrocarbon spark, current densities of 44 mA/cm2 were achieved at 20‐kV extractor voltage for an 8‐μs pulse. With an aluminum‐vapor arc, a current density of 15 mA/cm2 (0.3 A total) was measured for a 50‐μs pulse.

Generation and Measurements of Ion Species from Vacuum Arcs

We have measured the ion flux for different electrode materials in a vacuum arc. The vacuum arc has a point-plane geometry. The ion species in the generated plasma are identified using a time-of-flight (TOF) spectrometer. Ion species that have been generated to date include D+, Mg+, Mg++, Al+, Al++, Al+++, Ti+, Ti++, Ni+, Ni++, Cu+, Cu++, Zn+, Zn++, and In+. We found that in all cases, the ion flux measured is directly proportional to the interelectrode gap spacing and to the arc current. Typical current densities measured were ~300 mA · cm-2 at a distance of 10 cm from the gap for 150-¿s pulse. The study will be used for the development of a multiple-arc array source for application to intense ion beam generation.

Vacuum arc arrays for intense metal ion beam injectors

Abstract Arrays of vacuum arcs have been investigated as a high-flux source of metal ions. Twelve adjacent arcs have been ignited by a single trigger input. The ignition method consists of overvolting the interelectrode gap to 50 kV with a low-energy pulser; the method is compatible with high-repetition-rate operation. With aluminum electrodes, the flux of Al + available for extraction exceeded 1 A/cm 2 over a 0.2 ms pulse. The flux was uniform in space and reproducible. The arc arrays were developed as a source for an intense ion beam generator for application to materials surface modification.

Grid‐controlled plasma cathodes

Experiments are described on a plasma cathode with biased grids to prevent entry of ions into the electron extraction gap. The cathode has potential applications to the generation of high‐current pulsed electron beams. Operation at 20 A/cm2 is theoretically possible. The source combines the low average power consumption of a plasma cathode with many of the attractive features of thermionic cathodes, such as space‐charge‐limited extractor gap electron flow, fast turn‐on, and no diode closure. Initial experiments are reported at the 2 A/cm2 level for pulse lengths to 160 μs.

Focusing of high-perveance planar electron beams in a miniature wiggler magnet array

The transport of planar electron beams is a topic of increasing interest for applications to high-power, high-frequency microwave devices. This paper describes two- and three-dimensional simulations of electron-beam transport in a notched wiggler magnet array. The calculations include self-consistent effects of beam-generated fields. The simple notched wiggler configuration can provide vertical and horizontal confinement of high-perveance sheet electron beams with small transverse dimensions. The feasibility calculations address a beam system to drive a 95-GHz traveling-wave tube experiment under construction at Los Alamos National Laboratory, Los Alamos, NM.

RF tumour ablation: computer simulation and mathematical modelling of the effects of electrical and thermal conductivity.

This study determined the effects of thermal conductivity on RF ablation tissue heating using mathematical modelling and computer simulations of RF heating coupled to thermal transport. Computer simulation of the Bio-Heat equation coupled with temperature-dependent solutions for RF electric fields (ETherm) was used to generate temperature profiles 2 cm away from a 3 cm internally-cooled electrode. Multiple conditions of clinically relevant electrical conductivities (0.07–12 S m−1) and ‘tumour’ radius (5–30 mm) at a given background electrical conductivity (0.12 S m−1) were studied. Temperature response surfaces were plotted for six thermal conductivities, ranging from 0.3–2 W m−1 °C (the range of anticipated clinical and experimental systems). A temperature response surface was obtained for each thermal conductivity at 25 electrical conductivities and 17 radii (n = 425 temperature data points). The simulated temperature response was fit to a mathematical model derived from prior phantom data. This mathematical model is of the form (T = a + bRc expdR σ f expgσ) for RF generator-energy dependent situations and (T = h + k expmR + n exppσ) for RF generator-current limited situations, where T is the temperature (°C) 2 cm from the electrode and a, b, c, d, f, g, h, k, m, n and p are fitting parameters. For each of the thermal conductivity temperature profiles generated, the mathematical model fit the response surface to an r2 of 0.97–0.99. Parameters a, b, c, d, f, k and m were highly correlated to thermal conductivity (r2 = 0.96–0.99). The monotonic progression of fitting parameters permitted their mathematical expression using simple functions. Additionally, the effect of thermal conductivity simplified the above equation to the extent that g, h, n and p were found to be invariant. Thus, representation of the temperature response surface could be accurately expressed as a function of electrical conductivity, radius and thermal conductivity. As a result, the non-linear temperature response of RF induced heating can be adequately expressed mathematically as a function of electrical conductivity, radius and thermal conductivity. Hence, thermal conductivity accounts for some of the previously unexplained variance. Furthermore, the addition of this variable into the mathematical model substantially simplifies the equations and, as such, it is expected that this will permit improved prediction of RF ablation induced temperatures in clinical practice.

High current density plasma cathode

A grid‐controlled plasma cathode has been operated at high current density (15 A/cm2) using vacuum insulator breakdown as the plasma source. The insulator spark generates a highly reproducible, 6‐μs plasma pulse with density 1013 cm−3 at a distance of 6 cm. A number of sparks can be driven in parallel to supply large area plasma cathodes.