Minor fixes, rename "Ion Sound Wave" and "Ito Process"

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 $\vb{E}_1$,