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Diffstat (limited to 'source/know/concept/coulomb-logarithm/index.md')
| -rw-r--r-- | source/know/concept/coulomb-logarithm/index.md | 10 |
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}$$ |