High order fluid model for streamer discharges. II. Numerical solution and investigation of planar fronts

The high order fluid model developed in the preceding paper is employed here to study the propagation of negative planar streamer fronts in pure nitrogen. The model consists of the balance equations for electron density, average electron velocity, average electron energy and average electron energy flux. These balance equations have been obtained as velocity moments of Boltzmann's equation and are here coupled to the Poisson equation for the space charge electric field. Here the results of simulations with the high order model, with a PIC/MC (Particle in cell/Monte Carlo) model and with the first order fluid model based on the hydrodynamic drift-diffusion approximation are presented and compared. The comparison with the MC model clearly validates our high order fluid model, thus supporting its correct theoretical derivation and numerical implementation. The results of the first order fluid model with local field approximation, as usually used for streamer discharges, show considerable deviations. Furthermore, we study the inaccuracies of simulation results caused by an inconsistent implementation of transport data into our high order fluid model. We also demonstrate the importance of the energy flux term in the high order model by comparing with results where this term is neglected. Finally, results with an approximation for the high order tensor in the energy flux equation is found to agree well with the PIC/MC results for reduced electric fields up to 1000 Townsend, as considered in this work.Comment: 26 pages, 11 figure

Testicular dermoid cyst in a 14-year-old child

ДЕРМОИДНАЯ КИСТА /ДИАГНДЕРМОИД /ДИАГНЯИЧКИ /УЛЬТРАСОНДЕТИКЛИНИЧЕСКИЕ СЛУЧАИВ работе представлен клинический случай ребенка, 14 лет, с дермоидной кистой правого яичка. Образование впервые было выявлено при профилактическом осмотре в поликлинике. В последующем пациенту неоднократно проводилось ультразвуковое исследование наружных половых органов, при котором в верхнем полюсе правого яичка выявлялась неоднородная эхоструктура размерами 14 мм, 13,7 мм и 12 мм с четким, ровным контуром. Результаты иммуноферментного анализа крови не показали увеличение основных маркеров опухолевого процесса. При биохимическом тестировании крови отмечалось незначительное повышение уровня прямого билирубина и сывороточного железа. Для уточнения диагноза проведена магнитно-резонансная томография органов малого таза с внутривенным контрастированием. После проведения указанного обследования был выставлен диагноз "кистозное образование правого яичка". После проведения необходимых дополнительных диагностических мероприятий (УЗИ периферических лимфатических узлов, обследование брюшной полости с внутривенным контрастным усилением) выполнена операция, заключавшаяся в ревизии правой половины мошонки и удалении образования правого яичка. Интраоперационно по данным экспресс-биопсии диагностировалась дермоидная киста правого яичка, что подтвердилось при последующем гистологическом исследовании. Послеоперационный период протекал гладко. Пациент выписался в удовлетворительном состоянии. Таким образом, представленное клиническое наблюдение подчеркивает необходимость оптимизации профилактической работы медицинского персонала первичного звена по своевременной диагностике опухолевых процессов наружных половых органов, особенно у детей пубертатного возраста.The paper presents a clinical case of a 14-year-old child with a dermoid cyst of the right testicle. The formation was first detected during a routine check-up in the polyclinic. Then the external genitalia ultrasound examination was repeatedly performed to the patient, which revealed an inhomogeneous echostructure with dimensions of 14 mm, 13.7 mm and 12 mm with a clear, even contour in the upper pole of the right testicle. The enzyme-linked immunosorbent assay (ELISA) did not show an increase in the main tumour markers. The biochemical blood test revealed an insignificant rise in conjugated bilirubin and serum iron. To clarify the diagnosis, magnetic resonance tomography of the pelvic organs with intravenous contrast was recommended. After examination, the cystic lesion of the right testicle was diagnosed. After carrying out the necessary additional diagnostic measures (ultrasound examination of the peripheral lymphatic nodes, the abdominal cavity exploration with intravenous contrast enhancement), the child underwent an operation consisting in revising the right half of the scrotum and removing the formation of the right testicle. Intraoperatively, according to the express biopsy test, the dermoid cyst of the right testicle was diagnosed, which was confirmed by the subsequent histological examination. The postoperative period was uneventful. The patient was discharged in satisfactory state. Thus, the presented clinical observation emphasizes the need to optimize the preventive work of primary care medical personnel for timely diagnosis of tumor processes in the external genital organs, especially in children of puberty

Derivation and test of high order fluid model for streamer discharges

A high order fluid model for streamer dynamics is developed by closing the system after the 4th moment of the Boltzmann equation in local mean energy approximation. This is done by approximating the high order pressure tensor in the heat flux equation through the previous moments. Mathematical characteristics of the system is studied. Then planar ionization fronts for negative streamers in Nsub2 are simulated with the classical streamer model, MC-PIC particle model, and with the present higher order model

High order fluid model for streamer discharges

A high order fluid model for streamer discharges is developed and used to investigate propagation of negative streamer fronts in N2 . Mo- mentum transfer theory is employed to evaluate the collision terms and close the system of moment/balance equations. The results of simulations are compared with those obtained by a PIC/MC method and by the classical first order fluid model based on the drif

Comparing plasma fluid models of different order for 1D streamer ionization fronts

We evaluate the performance of three plasma fluid models: the first order reaction-drift-diffusion model based on the local field approximation; the second order reaction-drift-diffusion model based on the local energy approximation and a recently developed high order fluid model by Dujko et al (2013 J. Phys. D 46 475202) We first review the fluid models: we briefly discuss their derivation, their underlying assumptions and the type of transport data they require. Then we compare these models to a particle-in-cell/Monte Carlo (PIC/MC) code, using a 1D test problem. The tests are performed in neon and nitrogen at standard temperature and pressure, over a wide range of reduced electric fields. For the fluid models, transport data generated by a multi-term Boltzmann solver are used. We analyze the observed differences in the model predictions and address some of the practical aspects when using these plasma fluid models

Magnetic Properties of J-J-J' Quantum Heisenberg Chains with Spin S=1/2, 1, 3/2 and 2 in a Magnetic Field

By means of the density matrix renormalization group (DMRG) method, the magnetic properties of the J-J-J$^{\prime}$ quantum Heisenberg chains with spin $S=1/2$, 1, 3/2 and 2 in the ground states are investigated in the presence of a magnetic field. Two different cases are considered: (a) when $J$ is antiferromagnetic and $J^{\prime}$ is ferromagnetic (i.e. the AF-AF-F chain), the system is a ferrimagnet. The plateaus of the magnetization are observed. It is found that the width of the plateaus decreases with increasing the ferromagnetic coupling, and disappears when $$ passes over a critical value. The saturated field is observed to be independent of the ferromagnetic coupling; (b) when $J$ is ferromagnetic and $J^{\prime}$ is antiferromagnetic (i.e. the F-F-AF chain), the system becomes an antiferromagnet. The plateaus of the magnetization are also seen. The width of the plateaus decreases with decreasing the antiferromagnetic coupling, and disappears when $J^{\prime}/J$ passes over a critical value. Though the ground state properties are quite different, the magnetization plateaus in both cases tend to disappear when the ferromagnetic coupling becomes more dominant. Besides, no fundamental difference between the systems with spin half-integer and integer has been found.Comment: 8 pages, 9 figures, to be published in J. Phys.: Condens. Matte

Structure and morphology of low mechanical loss TiO₂-doped Ta₂O₅

The exceptional stability required from high finesse optical cavities and high precision interferometers is fundamentally limited by Brownian motion noise in the interference coatings of the cavity mirrors. In amorphous oxide coatings these thermally driven fluctuations are dominant in the high index layer compared to those in the low index SiO₂ layer in the stack. We present a systematic study of the evolution of the structural and optical properties of ion beam sputtered TiO₂-doped Ta₂O₅ films with annealing temperature. We show that low mechanical loss in TiO₂-doped Ta₂O₅ with a Ti cation ratio = 0.27 is associated with a material that consists of a homogeneous titanium-tantalum-oxygen mixture containing a low density of nanometer sized Ar-filled voids. When the Ti cation ratio is 0.53, phase separation occurs leading to increased mechanical loss. These results suggest that amorphous mixed oxides with low mechanical loss could be identified by considering the thermodynamics of ternary phase formation

Structure and morphology of low mechanical loss TiO₂-doped Ta₂O₅

The exceptional stability required from high finesse optical cavities and high precision interferometers is fundamentally limited by Brownian motion noise in the interference coatings of the cavity mirrors. In amorphous oxide coatings these thermally driven fluctuations are dominant in the high index layer compared to those in the low index SiO₂ layer in the stack. We present a systematic study of the evolution of the structural and optical properties of ion beam sputtered TiO₂-doped Ta₂O₅ films with annealing temperature. We show that low mechanical loss in TiO₂-doped Ta₂O₅ with a Ti cation ratio = 0.27 is associated with a material that consists of a homogeneous titanium-tantalum-oxygen mixture containing a low density of nanometer sized Ar-filled voids. When the Ti cation ratio is 0.53, phase separation occurs leading to increased mechanical loss. These results suggest that amorphous mixed oxides with low mechanical loss could be identified by considering the thermodynamics of ternary phase formation