Bootstrap current - Revision history

Admin at 10:34, 26 January 2023

2023-01-26T10:34:49Z

← Older revision		Revision as of 12:34, 26 January 2023
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	The difference in particle density on banana orbits crossing a given radial position ''r'' then leads to a net toroidal current at ''r''.		The difference in particle density on banana orbits crossing a given radial position ''r'' then leads to a net toroidal current at ''r''.
	The bootstrap current is estimated (roughly) as		The bootstrap current is estimated (roughly) as
	<ref>K. Miyamoto, ''Plasma Physics and Controlled Nuclear Fusion'', Springer-Verlag (2005) ISBN 3540242171</ref>		<ref>K. Miyamoto, ''Plasma Physics and Controlled Nuclear Fusion'', Springer-Verlag (2005) {{ISBN\|3540242171}}</ref>

	:<math>j_{b} \sim -\varepsilon^{1/2}\frac{1}{B_p}\frac{dp}{dr}</math>		:<math>j_{b} \sim -\varepsilon^{1/2}\frac{1}{B_p}\frac{dp}{dr}</math>

Admin at 10:24, 27 September 2009

2009-09-27T10:24:53Z

← Older revision		Revision as of 12:24, 27 September 2009
Line 3:		Line 3:
	The difference in particle density on banana orbits crossing a given radial position ''r'' then leads to a net toroidal current at ''r''.		The difference in particle density on banana orbits crossing a given radial position ''r'' then leads to a net toroidal current at ''r''.
	The bootstrap current is estimated (roughly) as		The bootstrap current is estimated (roughly) as
	<ref>K. Miyamoto, ''Plasma ~~physics~~ and ~~controlled nuclear fusion~~'', Springer (~~2004~~) ISBN ~~3-540-24217-1~~</ref>		<ref>K. Miyamoto, ''Plasma Physics and Controlled Nuclear Fusion'', Springer-Verlag (2005) ISBN 3540242171</ref>

	:<math>j_{b} \sim -\varepsilon^{1/2}\frac{1}{B_p}\frac{dp}{dr}</math>		:<math>j_{b} \sim -\varepsilon^{1/2}\frac{1}{B_p}\frac{dp}{dr}</math>

Admin at 09:28, 27 September 2009

2009-09-27T09:28:11Z

← Older revision		Revision as of 11:28, 27 September 2009
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	The bootstrap current is a [[Neoclassical transport\|Neoclassical]] toroidal current produced in the presence of a pressure gradient, associated with the existence of trapped (banana) particles.		The bootstrap current is a [[Neoclassical transport\|Neoclassical]] toroidal current produced in the presence of a pressure gradient, associated with the existence of trapped (banana) particles in toroidal magnetic confinement systems.
	These trapped particles must be able to complete their (banana) orbits, so a requirement for the existence of the bootstrap current is ν<sub>ei</sub> < ν<sub>b</sub> (the collision frequency is less than the banana bounce frequency).		These trapped particles must be able to complete their (banana) orbits, so a requirement for the existence of the bootstrap current is ν<sub>ei</sub> < ν<sub>b</sub> (the collision frequency is less than the banana bounce frequency).
	The difference in particle density on banana orbits crossing a given radial position ''r'' then leads to a net toroidal current at ''r''.		The difference in particle density on banana orbits crossing a given radial position ''r'' then leads to a net toroidal current at ''r''.

Admin at 07:48, 27 September 2009

2009-09-27T07:48:17Z

← Older revision		Revision as of 09:48, 27 September 2009
Line 1:		Line 1:
	The bootstrap current is a [[Neoclassical transport\|Neoclassical]] toroidal current produced in the presence of a pressure gradient, associated with the existence of trapped (banana) particles.		The bootstrap current is a [[Neoclassical transport\|Neoclassical]] toroidal current produced in the presence of a pressure gradient, associated with the existence of trapped (banana) particles.
	These trapped particles must be able to complete their (banana) orbits, so a requirement for the existence of the bootstrap current is ν<sub>ei</sub> < ν<sub>b</sub> (the collision frequency is less than the banana ~~orbit~~ frequency).		These trapped particles must be able to complete their (banana) orbits, so a requirement for the existence of the bootstrap current is ν<sub>ei</sub> < ν<sub>b</sub> (the collision frequency is less than the banana bounce frequency).
	The difference in particle density on banana orbits crossing a given radial position ''r'' then leads to a net toroidal current at ''r''.		The difference in particle density on banana orbits crossing a given radial position ''r'' then leads to a net toroidal current at ''r''.
	The bootstrap current is estimated (roughly) as		The bootstrap current is estimated (roughly) as

Admin: Created page with 'The bootstrap current is a Neoclassical toroidal current produced in the presence of a pressure gradient, associated with the existence of trapped (ban…'

2009-09-27T07:47:36Z

Created page with 'The bootstrap current is a Neoclassical toroidal current produced in the presence of a pressure gradient, associated with the existence of trapped (ban…'

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The bootstrap current is a [[Neoclassical transport|Neoclassical]] toroidal current produced in the presence of a pressure gradient, associated with the existence of trapped (banana) particles.
These trapped particles must be able to complete their (banana) orbits, so a requirement for the existence of the bootstrap current is νei < νb (the collision frequency is less than the banana orbit frequency).
The difference in particle density on banana orbits crossing a given radial position ''r'' then leads to a net toroidal current at ''r''.
The bootstrap current is estimated (roughly) as
<ref>K. Miyamoto, ''Plasma physics and controlled nuclear fusion'', Springer (2004) ISBN 3-540-24217-1</ref>

:<math>j_{b} \sim -\varepsilon^{1/2}\frac{1}{B_p}\frac{dp}{dr}</math>

Here, ε is the inverse aspect ratio ''a/R'', ''Bp'' the poloidal magnetic field, and ''p'' the pressure.
More precise estimates can be made by simulating particle orbits.

== References ==
<references />