From a8d31faecc733fa4d63fde58ab98a5e9d11029c2 Mon Sep 17 00:00:00 2001
From: Prefetch
Date: Sun, 2 Apr 2023 16:57:12 +0200
Subject: Improve knowledge base

---
 source/know/concept/boltzmann-relation/index.md | 16 ++++++++--------
 1 file changed, 8 insertions(+), 8 deletions(-)

(limited to 'source/know/concept/boltzmann-relation')

diff --git a/source/know/concept/boltzmann-relation/index.md b/source/know/concept/boltzmann-relation/index.md
index b528adf..b3634f3 100644
--- a/source/know/concept/boltzmann-relation/index.md
+++ b/source/know/concept/boltzmann-relation/index.md
@@ -8,15 +8,16 @@ categories:
 layout: "concept"
 ---
 
-In a plasma where the ions and electrons are both in thermal equilibrium,
-and in the absence of short-lived induced electromagnetic fields,
-their densities $$n_i$$ and $$n_e$$ can be predicted.
+In a plasma where the ions and electrons are in thermal equilibrium,
+in the absence of short-lived induced electromagnetic fields,
+the densities $$n_i$$ and $$n_e$$ can be predicted.
 
-By definition, a particle in an [electric field](/know/concept/electric-field/) $$\vb{E}$$
+By definition, a charged particle in
+an [electric field](/know/concept/electric-field/) $$\vb{E} = - \nabla \phi$$
 experiences a [Lorentz force](/know/concept/lorentz-force/) $$\vb{F}_e$$.
 This corresponds to a force density $$\vb{f}_e$$,
 such that $$\vb{F}_e = \vb{f}_e \dd{V}$$.
-For the electrons, we thus have:
+For electrons:
 
 $$\begin{aligned}
     \vb{f}_e
@@ -74,10 +75,9 @@ $$\begin{aligned}
 But due to their large mass,
 ions respond much slower to fluctuations in the above equilibrium.
 Consequently, after a perturbation,
-the ions spend more time in a transient non-equilibrium state
+the ions spend more time in a non-equilibrium state
 than the electrons, so this formula for $$n_i$$ is only valid
-if the perturbation is sufficiently slow,
-such that the ions can keep up.
+if the perturbation is sufficiently slow, such that the ions can keep up.
 Usually, electrons do not suffer the same issue,
 thanks to their small mass and hence fast response.
 
-- 
cgit v1.2.3