diff options
Diffstat (limited to 'content/know/concept/langmuir-waves/index.pdc')
| -rw-r--r-- | content/know/concept/langmuir-waves/index.pdc | 8 |
1 files changed, 4 insertions, 4 deletions
diff --git a/content/know/concept/langmuir-waves/index.pdc b/content/know/concept/langmuir-waves/index.pdc index cd9b449..3c3f1d2 100644 --- a/content/know/concept/langmuir-waves/index.pdc +++ b/content/know/concept/langmuir-waves/index.pdc @@ -34,7 +34,7 @@ We also need [Gauss' law](/know/concept/maxwells-equations/): $$\begin{aligned} \varepsilon_0 \nabla \cdot \vb{E} - = q_e (n_i - n_e) + = q_e (n_e - n_i) \end{aligned}$$ We split $n_e$, $\vb{u}_e$ and $\vb{E}$ into a base component @@ -85,10 +85,10 @@ and use the plasma's quasi-neutrality $n_i = n_{e0}$ to get: $$\begin{aligned} \varepsilon_0 \nabla \cdot \big( \vb{E}_0 \!+\! \vb{E}_1 \big) - = q_e (n_i - n_{e0} \!-\! n_{e1} ) + = q_e (n_{e0} + n_{e1} - n_i) \quad \implies \quad \varepsilon_0 \nabla \cdot \vb{E}_1 - = - q_e n_{e1} + = q_e n_{e1} \end{aligned}$$ Since we are looking for linear waves, @@ -110,7 +110,7 @@ Inserting this into the continuity equation and Gauss' law yields, respectively: $$\begin{aligned} - i \omega n_{e1} = - i n_{e0} \vb{k} \cdot \vb{u}_{e1} \qquad \quad - i \varepsilon_0 \vb{k} \cdot \vb{E}_1 = q_e n_{e1} + -\! i \varepsilon_0 \vb{k} \cdot \vb{E}_1 = q_e n_{e1} \end{aligned}$$ However, there are three unknowns $n_{e1}$, $\vb{u}_{e1}$ and $\vb{E}_1$, |