Description of heterogeneous plasma microfield and optical properties of plasma by the QUIP model

Optical properties of plasmas are determined by presence of fluctuating microscopic electric field. The present work provides thorough analysis of contemporary models and points out their shortcomings. To overcome the latter, we take the QUIP (QUasi-Independent Particles) model derived ab initio. We provide generalization of the model allowing to account for microfield heterogeneity up to octupole term. We investigate convergence of the multipole series and show that higher order terms can be neglected. The model does not require laborious computations because all formulae are rather simple and are given in explicit form. This fact is an advantage of the proposed model compared to other contemporary models. We perform verification of the model via comparison with experiments. We emphasize that the comparison should be made with respect to the number of observed lines because this number strongly depends on the selected model. We outline experiments suitable for such testing. These are the experiments on Ar+Kr radiating plasma heated by laser radiation. In these experiments, the entire Ar+16 spectral series is observed. The QUIP model correctly describes the number of observed lines of the series, so its adequateness is justified. © 2020 Elsevier Inc

Efficient Numerical Integration Methods for the Cauchy Problem for Stiff Systems of Ordinary Differential Equations

The notion of stiffness of a system of ordinary differential equations is refined. The main difficulties encountered when solving the Cauchy problem for stiff systems are indicated. The advantages of switching to a new argument, the integral curve arc length, are demonstrated. Various mesh step selection criteria are discussed, and the integral curve curvature criterion is recommended. The most reliable implicit and explicit schemes suitable for solving stiff problems are presented. A strategy permitting an asymptotically accurate computation of the error of a numerical solution simultaneously with the solution itself is described. An analysis of chemical kinetics of hydrogen combustion in oxygen with allowance for 9 components and 50 reactions between them is provided as an illustration. © 2019, Pleiades Publishing, Ltd

Verification of Microfield Models Using Dense Laser Plasma Specta

Abstract: Optical properties of dense plasma depend on electric fields inside it (the so-called microfield). A critical survey is made of existing theoretical models of plasma microfields. The most important models are verified using experiments in which dense plasma was created by powerful laser radiation. It is shown that the Quasi-Independent Particle model (QUIP) provides the best theoretical verification and agreement with experiments. © 2021, Allerton Press, Inc

Модель квазинезависимых частиц для неоднородного плазменного микрополя

Optical properties of plasmas are determined by presence of fluctuating microscopic electric field. The present work provides thorough analysis of contemporary models and points out their shortcomings. To overcome the latter, we take the QUIP (QUasi-Independent Particles) model derived ab initio. We provide generalization of the model allowing to account for microfield heterogeneity up to octupole term. We investigate convergence of the multipole series and and show that higher order terms can be neglected. We perform verification of the model via comparison with experiments. We emphasize that the comparison should be made with respect to the number of observed lines because this number strongly depends on the selected model. We outline experiments suitable for such testing. These are the experiments on Ar+Kr radiating plasma heated by laser radiation. In these experiments, the intire Ar+16 spectral series is observed. The QUIP model correctly describes the number of observed lines of the series, so its adequateness is justified.Оптические свойства плазмы определяются наличием в ней флуктуирующего микроскопического электрического поля. В работе дан критический анализ современных моделей микрополя и показаны их недостатки. Для преодоления этих недостатков взята модель QUIP (QUasi-Independent Particles), полученная из первых принципов. Построено ее обобщение, позволяющее учитывать неоднородность микрополя по октупольный член включительно. Исследована сходимость ряда по мультиполям и показано, что членами более высоких порядков можно пренебречь.Проведена апробация модели путем сравнения с экспериментами. Отмечено, что сравнение следует проводить по числу наблюдаемых линий в спектральных сериях, поскольку это число сильно зависит от принятой модели. Выбраны эксперименты, наиболее подходящие для такой проверки. Это эксперименты по свечению плазмы Ar+Kr, нагретой лазерным излучением, в которых видна полностью спектральная серия иона Ar+16. Показано, что обобщенная модель QUIP правильно описывает наблюдаемое число линий этой серии, что подтверждает ее адекватность

Solution of the Fredholm Equation of the First Kind by the Mesh Method with the Tikhonov Regularization

Abstract: We consider a linear ill-posed problem for the Fredholm equation of the first kind. For its regularization, Tikhonov’s stabilizer is implemented. To solve the problem, we use the mesh method, in which we replace integral operators by the simplest quadratures; and the differential ones, by the simplest finite differences. We investigate experimentally the influence of the regularization parameter and mesh thickening on the algorithm’s accuracy. The best performance is provided by the zeroth-order regularizer. We explain the reason of this result. We use the proposed algorithm for an applied problem of the recognition of two closely situated stars if the telescope instrument function is known. In addition, we show that the stars are clearly distinguished if the distance between them is ~0.2 of the instrumental function’s width and the values of brightness differ by 1–2 stellar magnitudes. © 2019, Pleiades Publishing, Ltd

Моделирование неоднородного плазменного микрополя

Optical properties of plasma are determined by presence of fluctuating micro-scopic electric field. In the present work, we construct a simple ab initio model of plasma microfield accounting for its heterogeneity up to octupole term for the first time. Comparison with experiments shows that only this model describes the observed number of spectral lines.Оптические свойства плазмы определяются наличием в ней флуктуирующего микроскопического электрического поля. В работе на основе первых принципов построена простая модель плазменного микрополя, впервые учитывающая его неоднородность по октупольный член включительно. Сравнение с экспериментами показало, что только эта модель микрополя правильно описывает наблюдаемое число линий в спектральных сериях

Simulation of an Inhomogeneous Plasma Microfield

Abstract: The optical properties of plasma are determined by the presence of a fluctuating microscopic electric field. A simple ab initio model of a plasma microfield accounting for its inhomogeneity up to an octupole term has been constructed for the first time. A comparison with experiments has shown that only this model correctly describes the observed number of spectral lines. © 2019, Pleiades Publishing, Ltd

Reciprocal Function Method for Cauchy Problems with First-Order Poles

Abstract: For the numerical solution of the Cauchy problem with multiple poles, we propose a reciprocal function method. In the case of first-order poles, it makes it possible to continue the solution through the poles and to determine the solution and the pole positions with good accuracy. The method allows one to employ conventional explicit and implicit schemes, for example, explicit Runge–Kutta schemes. A test problem with multiple poles is computed as an example. The proposed method is useful for construction of software for direct computation of special functions. © 2020, Pleiades Publishing, Ltd

Numerical solution of Cauchy problems with multiple poles of integer order

We consider Cauchy problem for ordinary differential equation with solution possessing a sequence of multiple poles. We propose the generalized reciprocal function method. It reduces calculation of a multiple pole to retrieval of a simple zero of accordingly chosen function. Advantages of this approach are illustrated by numerical examples. We propose two representative test problems which constitute interest for verification of other numerical methods for problems with poles.Рассмотрена задачи Коши для обыкновенного дифференциального уравнения с решением, обладающим последовательностью кратных полюсов целого порядка. Предложен обобщённый метод обратной функции, который сводит вычисление кратного полюса к расчёту простого нуля соответственно выбранной функции. Преимущества такого подхода проиллюстрированы на численных примерах. Предложены сложные тестовые задачи, которые представляют интерес для проверки других численных методов для задач с полюсами