User:Spiralwidget/sandbox: Difference between revisions – Wikipedia

 

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Over the course of this helical path, there is a positive skew in the location distribution of the charge carrier in the direction of the electric field, such that at any given point in time a measurement of the location of the charge carrier will on average result in a positive change from original position in the direction of the electric potential. During a collision with another particle in the medium, the velocity of the charge carrier is randomized at the point of collision. This location of collision is likely to be a positive change in the direction of the electric field from the original location of the charge carrier. After the velocity is randomised, the charge carrier will then restart helical motion from a different original location. Overall, this results in a bulk movement in the direction of the electric field such that a current is able to flow, which is known as the Pedersen Current, with the associated Pedersen Conductivity reaching a maximum when the frequency of collisions is approximately equal to the gyratory frequency so that the charge carriers experience one collision for every gyration, following the equation:{{Cite journal| doi = 10.1016/j.jastp.2013.12.013| issn = 1364-6826| volume = 115-116| pages = 79–86| last1 = Sheng| first1 = Cheng| last2 = Deng| first2 = Yue| last3 = Yue| first3 = Xinan| last4 = Huang| first4 = Yanshi| title = Height-integrated Pedersen conductivity in both E and F regions from COSMIC observations| journal = Journal of Atmospheric and Solar-Terrestrial Physics| series = Sun-Earth System Exploration: Moderate and Extreme Disturbances| accessdate = 2023-07-15| date = 2014-08-01| url = https://www.sciencedirect.com/science/article/pii/S1364682613003313}}

Over the course of this helical path, there is a positive skew in the location distribution of the charge carrier in the direction of the electric field, such that at any given point in time a measurement of the location of the charge carrier will on average result in a positive change from original position in the direction of the electric potential. During a collision with another particle in the medium, the velocity of the charge carrier is randomized at the point of collision. This location of collision is likely to be a positive change in the direction of the electric field from the original location of the charge carrier. After the velocity is randomised, the charge carrier will then restart helical motion from a different original location. Overall, this results in a bulk movement in the direction of the electric field such that a current is able to flow, which is known as the Pedersen Current, with the associated Pedersen Conductivity reaching a maximum when the frequency of collisions is approximately equal to the gyratory frequency so that the charge carriers experience one collision for every gyration, following the equation:{{Cite journal| doi = 10.1016/j.jastp.2013.12.013| issn = 1364-6826| volume = 115-116| pages = 79–86| last1 = Sheng| first1 = Cheng| last2 = Deng| first2 = Yue| last3 = Yue| first3 = Xinan| last4 = Huang| first4 = Yanshi| title = Height-integrated Pedersen conductivity in both E and F regions from COSMIC observations| journal = Journal of Atmospheric and Solar-Terrestrial Physics| series = Sun-Earth System Exploration: Moderate and Extreme Disturbances| accessdate = 2023-07-15| date = 2014-08-01| url = https://www.sciencedirect.com/science/article/pii/S1364682613003313}}

$$mathbf\{sigma\}\_P\; =\; frac\{en\_e\}B\; left\; \{\; sum\_i\; C\_i\; left\; [\; frac\{nu\_\{in\}\; /\; omega\_i\}\{1\; +\; (nu\_e^2\; /\; omega\_i^2)\}\; right\; ]\; +\; frac\{nu\_e\; /\; omega\_e\}\{1\; +\; (nu\_e^2\; /\; omega\_e^2)\}\; right\; \}$$

$$mathbf\{sigma\}\_P\; =\; frac\{en\_e\}B\; left\; \{\; sum\_i\; C\_i\; left\; [\; frac\{nu\_\{in\}\; /\; omega\_i\}\{1\; +\; (^2\; /\; omega\_i^2)\}\; right\; ]\; +\; frac\{nu\_e\; /\; omega\_e\}\{1\; +\; (nu\_e^2\; /\; omega\_e^2)\}\; right\; \}$$

Where where $n\_e$ is the electron density, $B$ is the magnetic field, $C\_i$ is the relative concentration of ion species i, $/nu\_\{in\}$ is the collision frequency between an ion of species i and neutral particles, $omega\_i$ is the ion gyrofrequency, $nu\_e$ is the sum of electron–ion and electron–neutral collision frequencies, and $omega\_e$ is the electron gyrofrequency.

Where where $n\_e$ is the electron density, $B$ is the magnetic field, $C\_i$ is the relative concentration of ion species i, $nu\_\{in\}$ is the collision frequency between an ion of species i and neutral particles, $omega\_i$ is the ion gyrofrequency, $nu\_e$ is the sum of electron–ion and electron–neutral collision frequencies, and $omega\_e$ is the electron gyrofrequency.

A negative charge carrier moves in the opposite direction to a positive charge carrier and has a drift instead in the direction -ExB, and undergo such a helical motion where there is a net negative skew in the distribution of position from the…