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# 物理代写|电动力学代考Electrodynamics代写|FY549 Tokamak plasma

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## 物理代写|电动力学代考Electrodynamics代写|Tokamak plasma

One can create a magnetic field with a solenoid wound around a cylindrical tube, and then roll the tube into a torus to prevent departure of particles along the magnetic field. A D Sakharov and I E Tamm in 1951 proposed a modified scheme formulating a theoretical basis for a thermonuclear reactor where the plasma would have a torus shape and be held by a magnetic field [15].

Such a trap was named a Tokamak, toroidal’naja kamera s magnitnymi katushkami (in Russian) [18]. Its essential element is a torus-mounted formatter that creates a vortex electric field causing a current in the plasma, which heats the plasma.

The plasma description via averaged (hydrodynamic) values of its parameters such as velocity is called magneto-hydro-dynamics (MHD). This complex name simply covers the notion of fluid (hydro) in movement (dynamics) in a magnetic field (magneto), which applies very precisely to what happens inside a tokamak. To confine a hot plasma in an immaterial container formed by the magnetic field lines is a bit like wanting to contain a gas under pressure in a tyre inner tube. See for more details http://physci.llnl.gov/Research/Tokamak/, the spherical alternative is presented in figure 7.3. The general view of the largest international project JET tokamak European Torus, built in England, is given in figure 7.4. The following records certain plasma parameters: temperature 320 million $\mathrm{K}$, concentration $4 \times 10^{20} \mathrm{~m}^{-3}$, energy retention time (see below) $1.8 \mathrm{~s}$. Magnetic field in this setup is almost $4 \mathrm{~T}$, so at a temperature of 100 million $\mathrm{K}$, ions Larmor, the measuring radius is $3.5 \mathrm{~mm}$.

Today (2020) the tokamak-ITER (‘The Way’ in Latin) project reaches its engineering height, being one of the most ambitious projects of energetics in the world to date. It intends to be the heart of the electric plant at the Cadarache facility [16], the ITER Tokamak will be the largest and most powerful fusion device in the world. It should achieve a deuterium-tritium plasma in which the reaction is sustained through internal heating.

## 物理代写|电动力学代考Electrodynamics代写|General remarks on plasma theoretical description

Generally plasma is a rich medium for waves initiation and propagation [26, 27]. As an example of plasma dynamics we choose a description of propagation of helicoidal waves in a model plasma with immobilized positive ions and movable electrons [27]. It is a good example to demonstrate some normal for plasma theory model approximations. The main difference with the previous section is an account of ions dynamics (via momentum balance). Namely such option is a natural step towards a closed matter-field description. We also restrict ourselves by the case of hydrodynamic approximation of the plasma interacting with electromagnetic field. Such description in a frame of small Knudsen numbers $K n=\frac{\nu_w}{\nu} \ll 1$ ( $\nu$ is collisions frequency, $\nu_w$ is a wave frequency), collisions between particles play a basic role, hence plasma may be considered as a conducting fluid. The electrodynamic equations are then in a correspondence with the hydrodynamic level description of particles. Starting with the first Maxwell’s equation (‘Coulomb law’)
$$\operatorname{div} \vec{E}=4 \pi \sum_a e_a n_a,$$
where $e_1=e_{-}$is electron charge and $n_1=n_{-}$denotes electron concentration, the rest indices values mark ions. Here the density of charge in equation (11.16) is written as the sum of ion densities with the charges factors account. Adding the absence of magnetic charges statement
$$\operatorname{div} \vec{B}=0$$
we reproduce Faraday’s law of section 6.1.1.
$$\operatorname{rot} \vec{E}=-\frac{1}{c} \frac{\partial \vec{B}}{\partial t},$$
and close the Maxwell system by the Maxwell-Ampère one
$$\operatorname{rot} \vec{B}=\frac{1}{c} \frac{\partial \vec{E}}{\partial t}+\frac{4 \pi}{c} \sum_a e_a n_a \vec{v}_a$$

# 电动力学代写

## 物理代写|电动力学代考Electrodynamics代奇|关于等离子体理论描述的一般意见

$$\operatorname{div} vec{E}=4 pisum_a e_a n_a,$$

$$\operatorname{div} vec{B}=0$$

$$\operatorname{rot} \vec{E}=-frac{1}{c}。\frac{partial vec{B}}{partial t}。$$

$$\ooperatorname{rot} \vec{B}=frac{1}{c}。\frac{partial vec{E}}{partial t}+frac{4 `pi}{c}。\sum_a e_a n_a \vec{v}_a$$

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。