Question

I would like to estimate the order of Kolmogorov scale

lk=(ν³ϵ_d)^{1/4}
of the plasma in solar corona, so I need to determine the viscosity ν and dissipation rate ϵ_d first.

I have read references and I found the viscosity can be estimate by assuming the Maxwellian distribution of the plasma electrons, which gives
ν∼(k_BT/nₑ)^{1/2}.

However, I haven't found ways to estimate the dissipation rate ϵd, which may be accessed by dimensional analysis: v³/L, but it is hard to determine these parameters.

Answer 1

To estimate the Kolmogorov scale (lk) of the plasma in the solar corona, use the following formulas:

`\[ \\u \approx \left((k_B T)/(n_e)\right)^(1/2) \]\[ \epsilon_d \approx (v^3)/(L) \]`

Substitute these values into the Kolmogorov scale formula:

`\[ l_k \approx \left(\\u^3 \epsilon_d\right)^(1/4) \]`

Step-by-step explanation:

In the quest to estimate the Kolmogorov scale (lk) of the solar corona plasma, the viscosity (ν) can be approximated by assuming a Maxwellian distribution for plasma electrons. This yields the expression:

`\[ \\u \approx \left((k_B T)/(n_e)\right)^(1/2) \]`

Here,
`\(k_B\)` is the Boltzmann constant, T is the temperature, and
`\(n_e\)` is the electron number density. This expression captures the characteristic speed of particle motion in the plasma.

On the other hand, determining the dissipation rate
`(\(\epsilon_d\))` involves dimensional analysis, where it can be expressed as
`\(v^3/L\)`, considering the characteristic velocity v and length scale L. Combining these, the Kolmogorov scale can be calculated using:

`\[ l_k \approx \left(\\u^3 \epsilon_d\right)^(1/4) \]`

This scale characterizes the smallest turbulent eddies in the plasma, providing insight into the energy cascade at small scales.

To summarize, estimating the Kolmogorov scale involves understanding the characteristic properties of the plasma, with viscosity and dissipation rate playing crucial roles. The provided formulas allow for a quantitative approach to grasp the intricacies of plasma dynamics in the solar corona.