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-rw-r--r--source/know/concept/coulomb-logarithm/index.md10
1 files changed, 5 insertions, 5 deletions
diff --git a/source/know/concept/coulomb-logarithm/index.md b/source/know/concept/coulomb-logarithm/index.md
index b843eb3..b3be5ac 100644
--- a/source/know/concept/coulomb-logarithm/index.md
+++ b/source/know/concept/coulomb-logarithm/index.md
@@ -147,12 +147,12 @@ We thus find:
$$\begin{aligned}
\boxed{
\sigma_\mathrm{small}
- = 8 \ln(\Lambda) \sigma_\mathrm{large}
- = \frac{q_1^2 q_2^2 \ln\!(\Lambda)}{2 \pi \varepsilon_0^2 |\vb{v}|^4 \mu^2}
+ = 8 \sigma_\mathrm{large} \ln(\Lambda)
+ = \frac{q_1^2 q_2^2 \ln(\Lambda)}{2 \pi \varepsilon_0^2 |\vb{v}|^4 \mu^2}
}
\end{aligned}$$
-Here, $$\ln\!(\Lambda)$$ is known as the **Coulomb logarithm**,
+Here, $$\ln(\Lambda)$$ is known as the **Coulomb logarithm**,
with the **plasma parameter** $$\Lambda$$ defined below,
equal to $$9/2$$ times the number of particles
in a sphere with radius $$\lambda_D$$:
@@ -168,7 +168,7 @@ $$\begin{aligned}
The above relation between $$\sigma_\mathrm{small}$$ and $$\sigma_\mathrm{large}$$
gives us an estimate of how much more often
small deflections occur, compared to large ones.
-In a typical plasma, $$\ln\!(\Lambda)$$ is between 6 and 25,
+In a typical plasma, $$\ln(\Lambda)$$ is between 6 and 25,
such that $$\sigma_\mathrm{small}$$ is 2-3 orders of magnitude larger than $$\sigma_\mathrm{large}$$.
Note that $$t$$ is now fixed as the period
@@ -179,7 +179,7 @@ for significant energy transfer between partices:
$$\begin{aligned}
\frac{1}{t}
= n |\vb{v}| \sigma_\mathrm{small}
- = \frac{q_1^2 q_2^2 \ln\!(\Lambda) \: n}{2 \pi \varepsilon_0^2 \mu^2 |\vb{v}|^3}
+ = \frac{q_1^2 q_2^2 \ln(\Lambda) \: n}{2 \pi \varepsilon_0^2 \mu^2 |\vb{v}|^3}
\sim \frac{n}{T^{3/2}}
\end{aligned}$$