From 521e6ff9f68366427a0638373148662814dd9bb8 Mon Sep 17 00:00:00 2001 From: Lugovtsov Gleb Date: Fri, 7 Oct 2022 11:52:10 +0300 Subject: [PATCH] Change project structure --- 3.2.5-oscillating-circuit/description.pdf | Bin 0 -> 1002893 bytes 3.2.5-oscillating-circuit/formulas.ipynb | 43 ---- .../{lab-3.2.5.zip => latex.zip} | Bin .../{lab_3_2_5.pdf => report.pdf} | Bin .../{lab-description.pdf => description.pdf} | Bin 3386423 -> 3386423 bytes .../latex-pattern/mipt_rus_png.png | Bin 14199 -> 0 bytes 3.5.1-ne-plasma/latex-pattern/preamble.tex | 49 ---- 3.5.1-ne-plasma/latex-pattern/titlepage.tex | 26 --- 3.5.1-ne-plasma/main.tex | 210 ------------------ 3.5.1-ne-plasma/{lab_3_5_1.pdf => report.pdf} | Bin 3.6.1-spectrum/description.pdf | Bin 0 -> 3325142 bytes 3.6.1-spectrum/latex-pattern/preamble.tex | 44 ---- 3.6.1-spectrum/latex-pattern/titlepage.tex | 26 --- 3.6.1-spectrum/main.tex | 209 ----------------- .../{ => raw-data}/progress_of_work.md | 0 3.6.1-spectrum/{lab_3_6_1.pdf => report.pdf} | Bin 16 files changed, 607 deletions(-) create mode 100644 3.2.5-oscillating-circuit/description.pdf delete mode 100644 3.2.5-oscillating-circuit/formulas.ipynb rename 3.2.5-oscillating-circuit/{lab-3.2.5.zip => latex.zip} (100%) rename 3.2.5-oscillating-circuit/{lab_3_2_5.pdf => report.pdf} (100%) rename 3.5.1-ne-plasma/{lab-description.pdf => description.pdf} (99%) delete mode 100644 3.5.1-ne-plasma/latex-pattern/mipt_rus_png.png delete mode 100644 3.5.1-ne-plasma/latex-pattern/preamble.tex delete mode 100644 3.5.1-ne-plasma/latex-pattern/titlepage.tex delete mode 100644 3.5.1-ne-plasma/main.tex rename 3.5.1-ne-plasma/{lab_3_5_1.pdf => report.pdf} (100%) create mode 100644 3.6.1-spectrum/description.pdf delete mode 100644 3.6.1-spectrum/latex-pattern/preamble.tex delete mode 100644 3.6.1-spectrum/latex-pattern/titlepage.tex delete mode 100644 3.6.1-spectrum/main.tex rename 3.6.1-spectrum/{ => raw-data}/progress_of_work.md (100%) rename 3.6.1-spectrum/{lab_3_6_1.pdf => 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-\usepackage{amsmath,amsfonts,amssymb,amsthm,mathrsfs,mathtools} - -\usepackage[some]{background} -\usepackage{paratype} - -\usepackage{cancel} -\usepackage{multirow} -\usepackage[colorlinks, linkcolor = blue]{hyperref} - - -\definecolor{titlepagecolor}{cmyk}{1,.60,0,.40} - -\DeclareFixedFont{\bigsf}{T2A}{PTSans-TLF}{b}{n}{1.4cm} - -\backgroundsetup{ -scale=1, -angle=0, -opacity=1, -contents={\begin{tikzpicture}[remember picture,overlay] - \path [fill=titlepagecolor] (-0.5\paperwidth,5) rectangle (0.5\paperwidth,10); -\end{tikzpicture}} -} - -\makeatletter - -\def\printauthor{% - {\large \@author}} -\makeatother - -\author{% - Луговцов Глеб\\ - ФЭФМ МФТИ\\ - \texttt{lugovtsov.gs@phystech.edu}\vspace{40pt}\\ - % Author 2 name \\ - % Department name \\ - % \texttt{email2@example.com} -} \ No newline at end of file diff --git a/3.5.1-ne-plasma/latex-pattern/titlepage.tex b/3.5.1-ne-plasma/latex-pattern/titlepage.tex deleted file mode 100644 index e8c90fe..0000000 --- a/3.5.1-ne-plasma/latex-pattern/titlepage.tex +++ /dev/null @@ -1,26 +0,0 @@ -\begin{titlepage} -\BgThispage -\newgeometry{left=1.5cm,right=3cm} -\vspace*{2cm} -\noindent -\textcolor{white}{\bigsf \artitle} -\vspace*{2cm}\par -\noindent -\begin{minipage}{0.48\linewidth} - \begin{flushright} - \printauthor - \end{flushright} -\end{minipage} \hspace{15pt} -% -\begin{minipage}{0.02\linewidth} - \rule{1pt}{175pt} -\end{minipage} \hspace{-15pt} -% -\begin{minipage}{0.65\linewidth} -\vspace{5pt} - \begin{abstract} - \arabstract - \end{abstract} -\end{minipage} -\end{titlepage} -\restoregeometry \ No newline at end of file diff --git a/3.5.1-ne-plasma/main.tex b/3.5.1-ne-plasma/main.tex deleted file mode 100644 index ba05126..0000000 --- a/3.5.1-ne-plasma/main.tex +++ /dev/null @@ -1,210 +0,0 @@ -\input{latex-pattern/preamble} - -\newcommand{\artitle}{Изучение плазмы газового\\[9pt] разряда в неоне} - -\newcommand{\arabstract}{В работе изучается плазма газового разряда в неоне, ВАХ разряда и описание свойств полученной плазмы с помощью некоторых параметров.} - -\newcommand{\imageheight}{8cm} - -\begin{document} - -\input{latex-pattern/titlepage} - -\section{Введение} -Плазмой называют четвёртое агрегатное состояние, при котором вещество (в нашем случае это неон) диссоциирует на газ из свободных ионов, электронов и нейтральных частиц, которые не распались. Поведение этого газа можно описать множеством параметров, таких как температура, плазменная частота, радиус Дебая, среднее число ионов в дебаевской сфере. В этой работе мы постараемся подробно изучить поведение плазмы на примере двойного зонда и разряда. - -\section{Теоретическая справка} - -\subsection*{Плазма} -В ионизированном газе поле ионов <<экранируется>> электронами. Для поля $\mathbf{E}$ и плотности $\rho$ электрического заряда -$$ -\text{div}~\mathbf{E} = 4 \pi \rho, -$$ -а с учётом сферической симметрии и $\mathbf{E} = -\text{grad}~\varphi$: -\begin{equation} - \dfrac{d^2 \varphi}{dr^2}+\dfrac{2}{r}\dfrac{d\varphi}{dr}=-4\pi \rho. -\end{equation} -Плотности заряда электронов и ионов (которые мы считаем бесконечно тяжёлыми и поэтому неподвижными) -\begin{equation} - \begin{array}{c} - \rho_e = -ne \cdot \exp\left(\dfrac{e\varphi}{kT_e}\right),\\ - \rho_i = ne. - \end{array} -\end{equation} -Тогда из $(1)$ в предположении $\dfrac{e\varphi}{kT_e} \ll 1$ получим -\begin{equation} - \varphi = \dfrac{Ze}{r}e^{-r/r_D}, -\end{equation} -где $r_D = \sqrt{\dfrac{kT_e}{4\pi n e^2}}$ -- \textit{радиус Дебая}. Среднее число ионов в сфере такого радиуса -\begin{wrapfigure}{r}{4cm} - \includegraphics[scale=0.5]{images/figure.png} - \caption{Плазменные колебания} -\end{wrapfigure} -\begin{equation} - N_D = n\dfrac{4}{3}\pi r_D^2. -\end{equation} -Теперь выделим параллелепипед с плотностью $n$ электронов, сместим их на $x$. Возникнут поверхностные заряды $\sigma = nex$, поле от которых будет придавать электронам ускорение: -$$ -\dfrac{d^2x}{dt^2}=-\dfrac{eE}{m}=-\dfrac{4\pi n e^2}{m}x. -$$ -Отсюда получаем \textit{плазменную (ленгмюровскую) частоту} колебаний электронов: -\begin{equation} - \omega_p = \sqrt{\dfrac{4\pi ne^2}{m}}. -\end{equation} -\subsection*{Одиночный зонд} -При внесении в плазму уединённого проводника -- \textit{зонда} -- с потенциалом, изначально равным потенциалу точки плазмы, в которую его помещают, на него поступают токи электроннов и ионов: -\begin{equation} - \begin{array}{c} - I_{e0} = \dfrac{n \langle v_e \rangle}{4}eS,\\ - I_{i0} = \dfrac{n \langle v_i \rangle}{4}eS, - \end{array} -\end{equation} -где $\langle v_e \rangle$ и $\langle v_i \rangle$ -- средние скорости электронов и ионов, $S$ -- площадь зонда, $n$ -- плотность электронов и ионов. Скорости электронов много больше скорости ионов, поэтому $I_{i0} \ll I_{e0}$. Зонд будет заряжаться до некоторого равновестного напряжения $-U_f$ -- \textit{плавающего потенциала}.\\ -\begin{wrapfigure}{r}{5.5cm} - \includegraphics[scale=0.5]{images/zond.png} - \caption{Вольт-амперная характеристика одиночного зонда} -\end{wrapfigure} -В равновесии ионный ток мало меняется, а электронный имеет вид -$$ -I_e = I_0 \exp\left( -\dfrac{eU_f}{kT_e} \right). -$$ -Будем подавать потенциал $U_\text{з}$ на зонд и снимать значение зондового тока $I_\text{з}$. Максимальное значение тока $I_{e\text{н}}$ -- электронный ток насыщения, а минимальное $I_{i\text{н}}$ -- ионный ток насыщения. Значение из эмпирической формулы Бомона: -\begin{equation} - I_{i\text{н}} = 0.4 neS \sqrt{\dfrac{2kT_e}{m_i}}. -\end{equation} -\subsection*{Двойной зонд} -Двойной зонд -- система из двух одинаковых зондов, расположенных на небольшом расстоянии друг от друга, между которыми создаётся разность потенциалов, меньшая $U_f$. Рассчитаем ток между ними вблизи $I=0$. При небольших разностях потенциалов ионные токи на оба зонда близки к току насыщения и компенсируют друг друга, а значит величина результирующего тока полностью связана с разностью электронных токов. Пусть потенциалы на зондах -$$ -U_1 = -U_f + \Delta U_1, -$$ -$$ -U_2 = -U_f + \Delta U_2. -$$ -Между зондами $U = U_2 - U_1 = \Delta U_2 - \Delta U_1$. -Через первый электрод -\begin{equation} - I_1 = I_{i\text{н}} + I_{e1} = I_{i\text{н}} - \dfrac{1}{4}neS\langle v_e\rangle \exp\left(-\dfrac{eU_f}{kT_e}\right)\exp\left(\dfrac{e\Delta U_1}{kT_e}\right)=I_{i\text{н}}\left(1 - \exp\left( \dfrac{e\Delta U_1}{kT_e} \right)\right). -\end{equation} -Аналогично через второй получим -\begin{equation} -I_2 = I_{i\text{н}}\left(1 - \exp\left( \dfrac{e\Delta U_2}{kT_e} \right)\right) -\end{equation} - -Из $(7)$ и $(8)$ с учётом последовательного соединение зондов ($I_1 = -I_2 = I)$: -$$ -\Delta U_1= \dfrac{kT_e}{e}\text{ln}\left(1 - \dfrac{I}{I_{i\text{н}}}\right) -$$ -$$ -\Delta U_2= \dfrac{kT_e}{e}\text{ln}\left(1 + \dfrac{I}{I_{i\text{н}}}\right) -$$ - -Тогда итоговые формулы для разности потенциалов и тока - -\begin{equation} - U = \dfrac{kT_e}{e}\text{ln}\dfrac{1 - I/I_{i\text{н}}}{1 + I/I_{i\text{н}}}, - I = I_{i\text{н}} \text{th}\dfrac{eU}{2kT_e}. -\end{equation} -Реальная зависимость выглядит несколько иначе и описывается формулой -\begin{wrapfigure}{l}{7cm} - \includegraphics[scale=0.8]{images/double_zond.png} - \caption{Вольт-амперная характеристика двойного зонда} - \vspace{+30pt} -\end{wrapfigure} -\begin{equation} - I = I_{i\text{н}} \text{th}\dfrac{eU}{2kT_e} + AU. -\end{equation} -Из этой формулы можно найти формулу для $T_e$: для $U=0$ мы найдём $I_{i\text{н}}$, продифференцируем в точке $U=0$ и с учётом $\text{th}~\alpha \approx \alpha$ при малых $\alpha$ и $A\rightarrow 0$ получим: -\begin{equation} - kT_e = \dfrac{1}{2}\dfrac{eI_{i\text{н}}}{\dfrac{dI}{dU}|_{U=0}}. -\end{equation} -\\ - -\section{Ход работы} -\subsection*{Описание установки} - -\begin{figure}[!h] - \centering - \includegraphics[scale=0.6]{images/scheme.png} - \caption{Принципиальная схема установки} - \label{fig:my_label} -\end{figure} - -Стеклянная газоразрядная трубка имеет холодный (ненакаливаемый) полый катод, три анода и \textit{геттерный} узел -- стеклянный баллон, на внутреннюю повехность которого напылена газопоглощающая плёнка (\textit{геттер}). Трубка наполнена изотопом неона $^22$Ne при давлении 2 мм рт. ст. Катод и один из анодом (I и II) с помощью переключателя $\Pi_1$ подключается через балластный резистор $R_\text{б}$ ($\approx 450$ кОм) к регулируемому ВИП с выкодным напряжением до 5 кВ.\\ -При подключении к ВИП анода-I между ним и катодом возникает газовый разряд. Ток разряда измеряется миллиамперметром $A_1$, а падение напряжения на разрядной трубке -- цифровым вольтметром $V_1$, подключённым к трубке черезе высокоомный (25 МОм) делитель напряжения с коэффициентом $(R_1+R_2)/R_2 = 10$.\\ -При подключении к ВИП анода-II разряд возникает в пространстве между катодом и анодом-II, где находятся двойной зонд, используемый для диагностики плазмы положительного столба. Зонды изготовлены из молибденовой проволоки диаметром $d = 0.2$ мм и имеют длину $l = 5.2$ мм. Они подключены к источнику питания GPS через потенциометр $R$. Переключатель $\Pi_2$ позволяет изменять полярность напряжения на зондах. Величина напряжения на зондах изменяеься с помощью дискретного переключателя <<$V$>> выходного напряжения источника питания и потенциометра $R$, а измеряется цифровым вольтметром $V_2$. Для измерения зондового тока используется мультиметр $A_2$. - - -\subsection*{Исследование ВАХ разряда} -Зажигаем плазму и строим ВАХ разряда в координатах $I_\text{р}(U_\text{р})$: - -\begin{figure}[!h] - \centering - \includegraphics[height=\imageheight]{images/vah-discharge.png} - \caption{ВАХ разряда} - \label{fig:vah-discharge} -\end{figure} - -По наклону того участка кривой, который приближен к линии, находим максимальное диффиренциальное сопротивление разряда $R_\text{диф}$ (обратный коэффициент прямой): - -\begin{equation} - R_\text{диф} = \dfrac{dU}{dI} = 33.0 \pm 1.5 \text{ кОм} -\end{equation} - -Сравнивная полученную кривую с рисунком \ref{fig:vah-dis-all} мы приходим к выводу, что состояние будет называться \textit{поднормальным тлеющим зарядом} (участок ГД). Полное описание есть на стр. 283 практикума. - -\begin{figure}[h] - \centering - \includegraphics[height=\imageheight]{images/vah_discharge_all.jpg} - \caption{Вольт-амперная характеристика разряда в неоне при давлении 1 торр. Пунктиром изображён пример нагрузочной прямой, соответствующей режиму нормального тлеющего разряда.} - \label{fig:vah-dis-all} -\end{figure} - -\newpage -\subsection*{Исследование зондовых характеристик} - -Построим зондовые характеристики для разных токов и отцентруем кривые: - -\begin{figure}[!h] - \centering - \includegraphics[height=\imageheight]{images/vah-probe.png} - \caption{ВАХ двойного зонда} - \label{fig:my_label} -\end{figure} - -\newpage -Определим асимптоты: - -\begin{figure} - \centering - \includegraphics{images/vah-probe-fit.png} - \caption{Асимптоты ВАХ зондов} - \label{fig:my_label} -\end{figure} - -И по точкам пересечения асимптот с осью ординат найдём ионный ток насыщения: - -\[I_{i\text{н}}^{5\text{В}} = 95.8 \pm 0.5 \text{ мкА},\] -\[I_{i\text{н}}^{3\text{В}} = 52.5 \pm 0.2 \text{ мкА},\] -\[I_{i\text{н}}^{1.5\text{В}} = 25.9 \pm 0.1 \text{ мкА}.\] - -Полученные данные занесём в таблицу: - -\begin{table}[h!] -\centering -\begin{tabular}{|c|c|c|c|c|c|c|} -\hline -$I_p$, мА & $T_e$, $10^4$ К & $n_e$, $10^{15}$ м$^{-3}$ & $\omega_p$, $10^4$ рад/c & $r_D$, $10^{-5}$ см & $N_D$ & $\alpha$, $10^{-7}$ \\ \hline -5.0 & $41\pm 4$ & $58\pm 6$ & $144\pm 10$ & $49\pm 3$ & 30 & 24\\ \hline -3.0 & $42\pm 4$ & $33\pm 4$ & $107\pm 9$ & $66\pm 5$ & 40 & 13\\ \hline -1.5 & $41\pm 6$ & $16\pm 2$ & $75\pm 8$ & $94 \pm 10$ & 57 & 7\\ \hline -\end{tabular} -\end{table} - -\section{Выводы} -Исследовав ВАХ разряда, мы пришли к выводу, что плазма находилась в состоянии \textit{поднормального тлеющего заряда}. - -При исследовании зондовых характеристик удалось выяснить, что плазма \textit{идеальна} и \textit{квазинейтральна.} - - - -\end{document} \ No newline at end of file diff --git a/3.5.1-ne-plasma/lab_3_5_1.pdf b/3.5.1-ne-plasma/report.pdf similarity index 100% rename from 3.5.1-ne-plasma/lab_3_5_1.pdf rename to 3.5.1-ne-plasma/report.pdf diff --git a/3.6.1-spectrum/description.pdf b/3.6.1-spectrum/description.pdf new file mode 100644 index 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