Question

Measurement of Alfven waves​

Answer 1

Answer:

hey mate!!

Explanation:

alfen waves:-in plasma physics, an Alfvén wave, named after Hannes Alfvén, is a type of magnetohydrodynamic wave in which ions oscillate in response to a restoring force provided by an effective tension on the magnetic field lines.

thanks!

Answer 2

Answer:

The low-frequency relative permittivity {\displaystyle \epsilon } \epsilon of a magnetized plasma is given by

{\displaystyle \epsilon =1+{\frac {1}{B^{2}}}c^{2}\mu _{0}\rho } \epsilon = 1 + \frac{1}{B^2}c^2 \mu_0 \rho

where {\displaystyle B\,} B\, is the magnetic field strength, {\displaystyle c} c is the speed of light, {\displaystyle \mu _{0}} \mu _{0} is the permeability of the vacuum, and {\displaystyle \rho =\Sigma n_{s}m_{s}} {\displaystyle \rho =\Sigma n_{s}m_{s}} is the total mass density of the charged plasma particles. Here, {\displaystyle s} s goes over all plasma species, both electrons and (few types of) ions.

Therefore, the phase velocity of an electromagnetic wave in such a medium is

{\displaystyle v={\frac {c}{\sqrt {\epsilon }}}={\frac {c}{\sqrt {1+{\frac {1}{B^{2}}}c^{2}\mu _{0}\rho }}}} v = \frac{c}{\sqrt{\epsilon}} = \frac{c}{\sqrt{1 + \frac{1}{B^2}c^2 \mu_0 \rho}}

or

{\displaystyle v={\frac {v_{A}}{\sqrt {1+{\frac {1}{c^{2}}}v_{A}^{2}}}}} v = \frac{v_A}{\sqrt{1 + \frac{1}{c^2}v_A^2}}

where

{\displaystyle v_{A}={\frac {B}{\sqrt {\mu _{0}\rho }}}} v_A = \frac{B}{\sqrt{\mu_0 \rho}}

is the Alfvén velocity. If {\displaystyle v_{A}\ll c} v_A \ll c, then {\displaystyle v\approx v_{A}} v \approx v_A. On the other hand, when {\displaystyle v_{A}\rightarrow c} {\displaystyle v_{A}\rightarrow c}, then {\displaystyle v\approx c} v \approx c. That is, at high field or low density, the velocity of the Alfvén wave approaches the speed of light, and the Alfvén wave becomes an ordinary electromagnetic wave.

Neglecting the contribution of the electrons to the mass density and assuming that there is a single ion species, we get

{\displaystyle v_{A}={\frac {B}{\sqrt {\mu _{0}n_{i}m_{i}}}}~~} v_A = \frac{B}{\sqrt{\mu_0 n_i m_i}}~~ in SI

{\displaystyle v_{A}={\frac {B}{\sqrt {4\pi n_{i}m_{i}}}}~~} v_A = \frac{B}{\sqrt{4 \pi n_i m_i}}~~ in Gauss

{\displaystyle v_{A}\approx (2.18\times 10^{11}\,{\mbox{cm/s}})\,(m_{i}/m_{p})^{-1/2}\,(n_{i}/{\rm {cm}}^{-3})^{-1/2}\,(B/{\rm {gauss}})} v_A \approx (2.18\times10^{11}\,\mbox{cm/s})\,(m_i/m_p)^{-1/2}\,(n_i/{\rm cm}^{-3})^{-1/2}\,(B/{\rm gauss})

where {\displaystyle n_{i}} n_{i} is the ion number density and {\displaystyle m_{i}} m_{i} is the ion mass.