On approximative linear Boltzmann transport equation for charged particles

2018 ◽  
Vol 28 (14) ◽  
pp. 2905-2939
Author(s):  
J. Tervo ◽  
P. Kokkonen ◽  
M. Frank ◽  
M. Herty

We present results on existence and positivity of solutions for a linear Boltzmann transport equation used for example in radiotherapy applications and more generally in charged particle transports. Therein, some differential cross-sections, that is, kernels of collision integral operators, may become hyper-singular. These collision operators need to be approximated for analytical and numerical treatments. Here, we present an approximation leading to pseudo-differential operators. The final approximation, for which the existence and positivity of solutions is shown, is an integro-partial differential operator which is known as Continuous Slowing Down Approximation (CSDA).

2018 ◽  
Vol 29 (1) ◽  
pp. 174
Author(s):  
Jasim Mohammed salih Ali

Abstract: In this work, we were calculate the electron diffusion coefficients, such as, the drift velocity, characteristic energy, and collision frequencies using the cross sections of the momentum transfer and inelastic for electrons in CO2 from figure(1) after solving the Boltzmann transport equation numerically using the Finite-Difference Method in gas medium through applied electric field at 300 oK. The theoretical predictions were obtained in agreement with the experimental values was publishered. Keyword: CO2 lasers, Boltzmann Transport Equation, RF Discharges, Transport coefficients, Plasma discharge, Drift velocity. الخلاصة: في هذا العمل ، تم حساب معاملات انتشار الالكترونات مثل سرعة الانجراف، الطاقة الميزة و ترددات التصادم باستعمال المقاطع العرضية المرنة وغير مرنة للالكترونات في غاز ثاني أوكسيد الكاربون CO2 من شكل (1) خلال حل معادلة الانتقال لبولتزمان عددياً باستخدام طريقة التفريق المحدد في وسط غازي بعد تسليط مجال كهربائي عليه عند درجة حرارة 300 كلفن . النتائج التي تم الحصول عليها تنبأ بأنها متوافقة مع النتائج العملية المنشورة. الكلمات المفتاحية : ليزرات CO2 ، معادلة الانتقال لبولتزمان ، نموذج التفريغ ، معاملات الانتقال ، تفريغ البلازما ، سرعة الانجراف.


2017 ◽  
Vol 139 (10) ◽  
Author(s):  
Ajit K. Vallabhaneni ◽  
Liang Chen ◽  
Man P. Gupta ◽  
Satish Kumar

Several studies have validated that diffusive Fourier model is inadequate to model thermal transport at submicron length scales. Hence, Boltzmann transport equation (BTE) is being utilized to improve thermal predictions in electronic devices, where ballistic effects dominate. In this work, we investigated the steady-state thermal transport in a gallium nitride (GaN) film using the BTE. The phonon properties of GaN for BTE simulations are calculated from first principles—density functional theory (DFT). Despite parallelization, solving the BTE is quite expensive and requires significant computational resources. Here, we propose two methods to accelerate the process of solving the BTE without significant loss of accuracy in temperature prediction. The first one is to use the Fourier model away from the hot-spot in the device where ballistic effects can be neglected and then couple it with a BTE model for the region close to hot-spot. The second method is to accelerate the BTE model itself by using an adaptive model which is faster to solve as BTE for phonon modes with low Knudsen number is replaced with a Fourier like equation. Both these methods involve choosing a cutoff parameter based on the phonon mean free path (mfp). For a GaN-based device considered in the present work, the first method decreases the computational time by about 70%, whereas the adaptive method reduces it by 60% compared to the case where full BTE is solved across the entire domain. Using both the methods together reduces the overall computational time by more than 85%. The methods proposed here are general and can be used for any material. These approaches are quite valuable for multiscale thermal modeling in solving device level problems at a faster pace without a significant loss of accuracy.


2014 ◽  
Vol 185 (6) ◽  
pp. 1747-1758 ◽  
Author(s):  
Wu Li ◽  
Jesús Carrete ◽  
Nebil A. Katcho ◽  
Natalio Mingo

2008 ◽  
Vol 35 (6) ◽  
pp. 1098-1108 ◽  
Author(s):  
A.G. Buchan ◽  
C.C. Pain ◽  
M.D. Eaton ◽  
R.P. Smedley-Stevenson ◽  
A.J.H. Goddard

2018 ◽  
Vol 777 ◽  
pp. 421-425 ◽  
Author(s):  
Chhengrot Sion ◽  
Chung Hao Hsu

Many methods have been developed to predict the thermal conductivity of the material. Heat transport is complex and it contains many unknown variables, which makes the thermal conductivity hard to define. The iterative solution of Boltzmann transport equation (BTE) can make the numerical calculation and the nanoscale study of heat transfer possible. Here, we review how to apply the iterative method to solve BTE and many linear systems. This method can compute a sequence of progressively accurate iteration to approximate the solution of BTE.


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