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Снимается ВАХ разряда в режиме поднормального тлеющего разряда. Получаются зондовые характеристики, рассчитываются параметры плазмы (например, $\omega_p$, $r_D$). +В работе изучена плазма газового разряда в неоне с помощью двойного зонда. Была получена ВАХ разряда в режиме поднормального тлеющего разряда. Получены зондовые характеристики, рассчитываются параметры плазмы (например, $\omega_p$, $r_D$). \section{Введение} @@ -45,140 +45,47 @@ нагревать газ, то сначала молекулы диссоциируют на атомы, а затем и атомы распадаются на электроны и ионы, так что газ становится ионизованным, представляя собой смесь из свободных электронов и ионов, -а также нейтральных частиц. Если степень ионизации газа (отношение -числа ионизованных атомов к их полному числу) оказывается достаточно -велика, то поведение заряженных частиц приобретает коллективный характер, -так что описание свойств среды не может быть сведено к описанию -обычного газа, содержащего некоторое количество отдельных заряженных -частиц. Такое состояние ионизованного газа и называется плазмой. Первое описание плазмы было дано в 1923 г. И. Ленгмюром. Современная физика термин "газовый разряд" трактует как не только процесс протекания тока через газ, но и любой процесс возникновения ионизации газа под действием внешнего поля. Это и планируется пронаблюдать в данной работе. +а также нейтральных частиц. Такое состояние газа нельзя описывать как обычный газ с некоторыми частицами, требуются дополнительные параметры, описывающие движение такого газа (плазмы). Определение таких параметров, как тип разряда и других основных характеристик, и является целью данной работы. -\section{Поставка задачи} -Получить вольт-амперную характеристику газового разряда, определить тип разряда. Рассчитать основные характеристики плазмы методом зондовых характеристик. - - -\section{Теоретические сведения} -Определяющими свойствами плазмы являются коллективный характер -её движения и квазинейтральность (равенство нулю средней плотности -заряда). Рассмотрим простейший вид коллективных плазменных -колебаний. - -\begin{equation} -\label{w_p} -\omega_p=\sqrt{\frac{4\pi n_e e^2}{m_e}} -\end{equation} -$\omega_p$ - плазменная частота (частота коллективных колебаний электронов относительно квазинейтрального состояния, так называемых ленгмюровских колебаний, определяет временной масштаб для плазмы) - -Плазменный масштаб плазменных явлений задается дебаевским радиусом - амплитудой ленгмюровских колебаний, возбуждаемых тепловыми колебаниями -\begin{equation} -r_D = \sqrt{\frac{k_Б T_e}{4\pi n_e e^2}} -\end{equation} - -Рассмотрим плазменное экранирование. В равновесную плазму ($T = T_e = T_i$) помещена массивная пробная частица заряда $+q$, с радиусом, большим $r_D$. Для электронов из закона Больцмана: -\begin{equation} -n_e = n_{e0}\cdot \exp(\frac{e\varphi}{k_Б T}) -\end{equation} - -Аналогичное соотношение можно написать и для ионов (однозарядных). Температура электронов достаточно высока, поэтому: -\begin{equation} -\rho = -en_e+en_i\approx -en\cdot \frac{e\varphi}{k_Б T} -\end{equation} - -Уравнение Пуассона для одномерного случая: -\begin{equation} -\frac{d^2 \varphi}{dx^2}=-4\pi \rho -\end{equation} - -Объединив два уравнения, получим аналогичное выражение: -\begin{equation} -r_D = \sqrt{\frac{k_Б T_e}{4\pi n_e e^2}} -\end{equation} - -Теперь рассмотрим неравновесную плазму ($T_e\neq T_i$): -\begin{equation} -\label{R_De} -r_{De} = \sqrt{\frac{k_Б T_e}{4\pi n_e e^2}}, \hspace{2mm} -r_{Di} = \sqrt{\frac{k_Б T_i}{4\pi n_i e^2}} -\end{equation} - -Поэтому в общем случае: -\begin{equation} -\label{r_D_общ} -r_D = (r_{De}^2+r_{Di}^2)^{-1/2} = \sqrt{\frac{k_Б}{4\pi n_e e^2}\frac{T_eT_i}{T_e+T_i}}= -\end{equation} - -Плазма - ионизированный газ, $r_D \ll a$, размера области, занимаемой газом. -Плазма идеальна, если кулоновская энергия мала по сравнению с тепловой: -\begin{equation} -\omega_{кул} = -\frac{1}{2}n_i\frac{q^2}{r_D}, \hspace{2mm} \omega_{тепл} = n_ik_БT -\end{equation} - -Отношение энергий есть число заряженных частиц в сфере с дебаевским радиусом: -\begin{equation} -\label{N_D} -N_D = \frac{4}{3}\pi n_ir^3_D -\end{equation} - -Плазма идеальна при $N_D\gg1$. \section{Методика измерений} -\subsection{Плавающий потенциал} -Измерение электрических потенциалов с помощью "зондов" - небольших проводников, вводимых в плазму. При внесении проводника в плазму, он подвергается "бомбардировке" со стороны её заряженных частиц. Из-за различий в скорости частиц проводник зарядится отрицательно с потенциалов (отн. плазмы) $-U_f$ - плавающий потенциал. -Если бы $U_f = 0$: -\begin{equation}\label{i_0} -I_{e0} = \frac{n\bar{\upsilon_e}}{4}eS, \hspace{2mm} I_{i0} = \frac{n\bar{\upsilon_i}}{4}eS, -\end{equation} -Теперь $U_f \neq 0$: $I_i \approx I_{i0}$, согласно распределению Больцмана: -\begin{equation} -I_e = I_{e0} \exp(\frac{eU_f}{k_БT_e}) -\end{equation} - -\subsection{Одиночный зонд} -Схема измерений приведена на рис. \ref{одиночный}. -\begin{figure}[h!] -\includegraphics[width=0.3\textwidth]{Одиночный} -\caption{Исследование плазмы методом одиночного зонда} \label{одиночный} -\end{figure} - -Зависимость тока через зонд от потенциала зонда - зондовая характеристика (рис. \ref{зондовая_характеристика}). -\begin{figure}[h!] -\includegraphics[width=0.3\textwidth]{Зондовая_характеристика} -\caption{Зондовая характеристика} \label{зондовая_характеристика} -\end{figure} -Токи можно оценить из формулы \ref{i_0}: -\begin{equation} -I_{ен} \approx I_{e0} = \frac{1}{4}n_eS\sqrt{\frac{8k_БT_e}{\pi m_e}} -\end{equation} -Полуэмпирическая формула Д. Бома: -\begin{equation} -\label{бом} -I_{iн} \approx 0.4 n_iS\sqrt{\frac{2k_БT_e}{m_i}} -\end{equation} - -\subsection{Двойной зонд} -Двойной зонд - система, состоящая из двух одинаковых зондов на небольшом растоянии друг от друга, между которыми создается небольшая (по сравнению с $U_f$) разность потенциалов $U$. При малых токах через зонд: -\begin{equation} -U_1 = U_f +\Delta U_1, \hspace{2mm} U_2 = U_f +\Delta U_2 -\end{equation} -\begin{equation} -U = U_2 - U_1 = \Delta U_2 -\Delta U_1 -\end{equation} -Токи, приходящие на электроды: -\begin{equation} -I_1 = I_{iн}(1-\exp(\frac{e\Delta U_1}{k_БT_e})), \hspace{2mm} -I_2 = I_{iн}(1-\exp(\frac{e\Delta U_2}{k_БT_e})) -\end{equation} -Из последовательного соединения зондов: +Измерения произведены с помощью двойного зонда - системы, состоящей из двух одинаковых зондов на небольшом растоянии друг от друга, между которыми создается небольшая (по сравнению с потенциалом, до которого заряжается зонд, помещенный в плазму) разность потенциалов $U$. Теоретически получена зависимость тока от напряжения между зондами: (она также представлена на графике \ref{двойной}). \begin{equation} I = I_{iн} th\frac{eU}{2k_БT_e} \end{equation} -Вблизи $U = 0$: +\begin{figure}[h!] +\begin{center} +\includegraphics[width=0.6\textwidth]{Двойной} +\caption{Вольт-амперная характеристика двойного зонда} \label{двойной} +\end{center} +\end{figure} + +При рассмотрении этой формулы вблизи $U = 0$: \begin{equation} \label{двойной_зонд} k_БT_e = \frac{1}{2}\frac{eI_{iн}}{\frac{dI}{dU}|_{U=0}} \end{equation} +Из пересечения асимптот с с осью $U=0$ можно найти $I_{in}$. Далее, вычислив наклон графика в в начале координат, можно определить температуру электронов (формула \ref{двойной_зонд}). По этим известным параметрам можно найти концентрацию заряженных частиц, используя полуэмперическую формулу Д. Бома: +\begin{equation} +\label{бом} +I_{iн} \approx 0.4 n_iS\sqrt{\frac{2k_БT_e}{m_i}} +\end{equation} +Основными характеристиками плазмы являются плазменная частота колебаний $\omega_p$ (определяет временной масштаб движения плазмы), дебаевский радиус $r_{De}$ (определяет пространственный масштаб явления в плазме), поляризационная длина $r_D$ (определяет масштаб, на котором можно считать плазму квазинейтральной), среднее число ионов в дебаевской сфере $N_D$ (при больших значениях плазма считается идеальной). Теоретические формулы для вычисление этих величин приведены в таблице \ref{формулы}. +\begin{table}[h!] +\caption{Теоретические выражения для основных характеристик плазмы} +\label{формулы} +\begin{tabular}{|l|l|} +\hline +Величина & Теоретическое выражение \\ \hline +$\omega_p$ & $\sqrt{\frac{4\pi n_e e^2}{m_e}}$ \\ \hline +$r_{De} $ & $\sqrt{\frac{k_Б T_e}{4\pi n_e e^2}}$ \\ \hline +$r_D $ & $\sqrt{\frac{k_Б}{4\pi n_e e^2}\frac{T_eT_i}{T_e+T_i}}$ \\ \hline +$N_D $ & $\frac{4}{3}\pi n_ir^3_D$ \\ \hline +\end{tabular} +\end{table} -\subsection{Установка} +\section{Установка} Схема экспериментальной установки приведена на рисунке \ref{установка}. Трубка наполнена изотопом неона $^{22}Ne$ при давлении 2 мм рт. ст. 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 — вольтметром $V_1$. При подключении к ВИП анода-II разряд возникает в пространстве между катодом и анодом-II, где находится двойной зонд, используемый для диагностики плазмы положительного столба. @@ -197,20 +104,20 @@ k_БT_e = \frac{1}{2}\frac{eI_{iн}}{\frac{dI}{dU}|_{U=0}} \begin{figure}[h!] \begin{center} \includegraphics[width=\textwidth]{U(I)_discharge} -\caption{ВАХ разряда} \label{ВАХ_разряда} +\caption{Вольт-амперная характеристика разряда при давлении $P \sim$ 2 торр} \label{ВАХ_разряда} \end{center} \end{figure} По наклону кривой определили максимальное $R_{диф}=\frac{dU}{dI} = -68000 \pm 11000$ Ом. Полученный участок ВАХ соответствует поднормальному тлеющему разряду. \subsection{Зондовые характеристики} -При фиксированном токе разряда измерили вольт-амперную характеристику двойного зонда. (рис. \ref{ВАХ_зонда}). Для каждой зондовой характеристики определили ионный ток и наклон характеристики в начале координат по графику. Из полученных результатов рассчитаны $T_e$ (ф-ла \ref{двойной_зонд}), $n_i$ (ф-ла \ref{бом}), $\omega_p$ (ф-ла \ref{w_p}), $r_{De}$ (ф-ла \ref{R_De}) , $r_D$(ф-ла \ref{r_D_общ}), $N_D$ (ф-ла \ref{N_D}), $\alpha$ - степень ионизации плазмы. Результаты приведены в таблице \ref{data}, также построены графики зависимости +При фиксированном токе разряда измерили вольт-амперную характеристику двойного зонда. (рис. \ref{ВАХ_зонда}). Для каждой зондовой характеристики определили ионный ток и наклон характеристики в начале координат по графику. Из полученных результатов рассчитаны $T_e$, $n_i$, $\omega_p$, $r_{De}$, $r_D$, $N_D$, $\alpha$ - степень ионизации плазмы (по формулам из таблицы \ref{формулы}). Результаты приведены в таблице \ref{data}, также построены графики зависимости электронной температуры и концентрации электронов от тока разряда (рис. \ref{от_тока_разряда}). \begin{figure}[h!] \begin{center} \includegraphics[width=\textwidth]{I(U)_probe} -\caption{ВАХ двойного зонда} \label{ВАХ_зонда} +\caption{Вольт-амперная характеристика двойного зонда при небольших токах, давлении $P \sim$ 2 торр} \label{ВАХ_зонда} \end{center} \end{figure} @@ -233,7 +140,7 @@ $\alpha, 10^{-5}$ & $ 3.9 \pm 0.4 $ & $ 11.6 \pm 0.3 $ & $ 10.7 \pm 1. \begin{figure}[h!] \begin{center} \includegraphics[width=\textwidth]{T,n(I_p)} -\caption{Зависимость электронной температуры и концентрации электронов от тока разряда} \label{от_тока_разряда} +\caption{Зависимость электронной температуры и концентрации электронов от тока разряда при давлении $P \sim$ 2 торр} \label{от_тока_разряда} \end{center} \end{figure} @@ -258,6 +165,6 @@ $\alpha, 10^{-5}$ & $ 3.9 \pm 0.4 $ & $ 11.6 \pm 0.3 $ & $ 10.7 \pm 1. \section{Выводы} Из ВАХ разряда подтверждено, что исследуется тлеющий газовый разряд. -Экспериментальная зондовая характеристика подтверждает теоретическую зависимость: $I = I_{iн} th\frac{eU}{2k_БT_e}$, количество ионов в дебаевской сфере $N_D \sim 40$ показывает идеальность плазмы. Остальные характеристики плазмы получились схожими по порядку с примерами в инструкции к работе, что подтверждает справедливость метода измерений. Однако не удалось оценить зависимость температуры электронов от тока разряда из-за неточных измерений и малого их числа. +Экспериментальная зондовая характеристика схожа с теоретической зависимостью: $I = I_{iн} th\frac{eU}{2k_БT_e}$, количество ионов в дебаевской сфере $N_D \sim 40$ показывает идеальность плазмы. Остальные характеристики плазмы получились схожими по порядку с примерами в инструкции к работе, что подтверждает справедливость метода измерений. Однако не удалось оценить зависимость температуры электронов от тока разряда из-за неточных измерений и малого их числа. \end{document} \ No newline at end of file