Neoclassical transport - Revision history

Admin at 10:42, 26 January 2023

2023-01-26T10:42:33Z

← Older revision		Revision as of 12:42, 26 January 2023
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	The '''Neoclassical Transport Model''' is one of the pillars of the physics of magnetically confined plasmas.		The '''Neoclassical Transport Model''' is one of the pillars of the physics of magnetically confined plasmas.
	<ref>F.L. Hinton and R.D. Hazeltine, [[doi:10.1103/RevModPhys.48.239\|Rev. Mod. Phys. '''48''', 239 (1976)]]</ref>		<ref>F.L. Hinton and R.D. Hazeltine, [[doi:10.1103/RevModPhys.48.239\|Rev. Mod. Phys. '''48''', 239 (1976)]]</ref>
	<ref>P. Helander and D.J. Sigmar, ''Collisional Transport in Magnetized Plasmas'', Cambridge University Press (2001) ISBN 0521807980</ref>		<ref>P. Helander and D.J. Sigmar, ''Collisional Transport in Magnetized Plasmas'', Cambridge University Press (2001) {{ISBN\|0521807980}}</ref>
	It provides a model for the transport of particles, momentum, and heat due to Coulomb collisions in confined plasmas in complex magnetic geometries, assuming that the plasma is in a quiescent state.		It provides a model for the transport of particles, momentum, and heat due to Coulomb collisions in confined plasmas in complex magnetic geometries, assuming that the plasma is in a quiescent state.
	Thus, transport due to fluctuations lies outside of the scope of the theory.		Thus, transport due to fluctuations lies outside of the scope of the theory.
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	The main goal of Neoclassical transport theory is to provide a closed set of equations for the time evolution of these moments, for each particle species. Since the determination of any moment requires knowledge of the next order moment, this requires truncating the set of moments (''closure'' of the set of equations).		The main goal of Neoclassical transport theory is to provide a closed set of equations for the time evolution of these moments, for each particle species. Since the determination of any moment requires knowledge of the next order moment, this requires truncating the set of moments (''closure'' of the set of equations).
	<ref>T.J.M. Boyd and J.J. Sanderson, ''The physics of plasmas'', Cambridge University Press (2003) ISBN 0521459125</ref>		<ref>T.J.M. Boyd and J.J. Sanderson, ''The physics of plasmas'', Cambridge University Press (2003) {{ISBN\|0521459125}}</ref>

	It is customary to make a number of additional assumptions to facilitate the analysis: e.g., small gyroradius, nested magnetic surfaces, large parallel transport, Maxwellian distribution functions, etc.		It is customary to make a number of additional assumptions to facilitate the analysis: e.g., small gyroradius, nested magnetic surfaces, large parallel transport, Maxwellian distribution functions, etc.

Jlvelasco: /* Limitations */

2018-05-22T13:25:18Z

Limitations

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	* Maxwellianity. This assumption implies that a certain minimum level of [[Collisionality\|collisionality]] is needed in order to ensure that Maxwellianisation is effective. The strong drives and resulting gradients that characterise fusion-grade plasmas often lead to a violation of this assumption.		* Maxwellianity. This assumption implies that a certain minimum level of [[Collisionality\|collisionality]] is needed in order to ensure that Maxwellianisation is effective. The strong drives and resulting gradients that characterise fusion-grade plasmas often lead to a violation of this assumption.
	* A fixed geometry. Neoclassical transport is calculated in a static magnetic geometry. In actual experiments (especially Tokamaks), the magnetic field evolves along with the plasma itself, leading to a modification of net transport. While a slow evolution (with respect to typical transport time scales) should not be problematic, rapid changes (such as magnetic reconnections) are outside of the scope of the theory.		* A fixed geometry. Neoclassical transport is calculated in a static magnetic geometry. In actual experiments (especially Tokamaks), the magnetic field evolves along with the plasma itself, leading to a modification of net transport. While a slow evolution (with respect to typical transport time scales) should not be problematic, rapid changes (such as magnetic reconnections) are outside of the scope of the theory.
	* The linearity of the model. Neoclassical theory is a linear theory in which profiles are computed from sources, boundary conditions, and transport coefficients (that depend linearly on the profiles). No non-linear feedback of the profiles on the transport coefficients is contemplated. However, there are many experimental studies that show that the profiles feed back non-linearly on transport (via [[TJ-II:Turbulence\|turbulence]]), leading to some degree of [[Self-Organised Criticality\|self-organisation]].		* The linearity of the model. Neoclassical theory is a linear theory in which profiles are computed from sources, boundary conditions, and transport coefficients (that depend linearly on the profiles). No non-linear feedback of the profiles on the transport coefficients is not usually contemplated. However, there are many experimental studies that show that the profiles feed back non-linearly on transport (via [[TJ-II:Turbulence\|turbulence]]), leading to some degree of [[Self-Organised Criticality\|self-organisation]].
	* Locality. Neoclassical theory is a theory of diffusion, and therefore it assumes that particle motion between collisions is small with respect to any other relevant spatial scales. This assumption then allows writing down differential equations, expressing the fluxes in terms of ''local'' gradients. This basic assumption is violated under specific conditions, which may include: (a) the low-collisionality limit, (b) any situation in which the gradient scale length is very small (e.g., [[Internal Transport Barrier]]s), (c) locations close to the plasma edge<ref>T. Fülöp, P. Helander, [[doi:10.1063/1.1372179\|Phys. Plasmas 8, 3305 (2001)]]</ref><ref>V. Tribaldos and J. Guasp, ''Neoclassical global flux simulations in stellarators'', [[doi:10.1088/0741-3335/47/3/010\|Plasma Phys. Control. Fusion '''47''' (2005) 545]]</ref>, and (d) particles transported in ''streamers''. Such phenomena could give rise to [[Non-diffusive transport\|super-diffusion]]. Points (a) through (c) can be handled by using a Monte Carlo or Master Equation approach instead of deriving differential equations.		* Locality. Neoclassical theory is a theory of diffusion, and therefore it assumes that radial particle motion between collisions is small with respect to any other relevant spatial scales. This assumption then allows writing down differential equations, expressing the fluxes in terms of ''local'' gradients. This basic assumption is violated under specific conditions, which may include: (a) the low-collisionality limit, (b) any situation in which the gradient scale length is very small (e.g., [[Internal Transport Barrier]]s), (c) locations close to the plasma edge<ref>T. Fülöp, P. Helander, [[doi:10.1063/1.1372179\|Phys. Plasmas 8, 3305 (2001)]]</ref><ref>V. Tribaldos and J. Guasp, ''Neoclassical global flux simulations in stellarators'', [[doi:10.1088/0741-3335/47/3/010\|Plasma Phys. Control. Fusion '''47''' (2005) 545]]</ref>, and (d) particles transported in ''streamers''. Such phenomena could give rise to [[Non-diffusive transport\|super-diffusion]]. Points (a) through (c) can be handled by using a Monte Carlo or Master Equation approach instead of deriving differential equations.
	* Markovianity. A second assumption underlying diffusive models (including Neoclassics) is Markovianity, implying that the motion of any particle is only determined by its current velocity and position. However, there are situations, such as stochastic magnetic field regions, persistent turbulent eddies, or transport barriers, where this assumption may be violated (due to trapping effects, so that the preceding history of the particle trajectory becomes important). Typically, this would then give rise to [[Non-diffusive transport\|sub-diffusion]].		* Markovianity. A second assumption underlying diffusive models (including Neoclassics) is Markovianity, implying that the motion of any particle is only determined by its current velocity and position. However, there are situations, such as stochastic magnetic field regions, persistent turbulent eddies, or transport barriers, where this assumption may be violated (due to trapping effects, so that the preceding history of the particle trajectory becomes important). Typically, this would then give rise to [[Non-diffusive transport\|sub-diffusion]].

	== References ==		== References ==
	<references />		<references />

Jlvelasco at 13:23, 22 May 2018

2018-05-22T13:23:18Z

← Older revision		Revision as of 15:23, 22 May 2018
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	Neoclassical models have been used with success to predict transport under certain specific conditions.		Neoclassical models have been used with success to predict transport under certain specific conditions.
	''(Citation needed)''		''(Citation needed)''
	The [[Bootstrap current\|bootstrap current]] predicted by the theory is confirmed experimentally, both qualitatively and quantitatively.		The [[Bootstrap current\|bootstrap current]] and radial electric field predicted by the theory are confirmed experimentally, both qualitatively and quantitatively in most scenarios.
	''(Citation needed)''		''(Citation needed)''
	In experimental studies, Neoclassical transport estimates are often used as a "baseline" transport level -		In experimental studies, Neoclassical transport estimates are often used as a "baseline" transport level -

Admin: Updated reference links

2018-04-03T13:52:35Z

Updated reference links

← Older revision		Revision as of 15:52, 3 April 2018
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	The '''Neoclassical Transport Model''' is one of the pillars of the physics of magnetically confined plasmas.		The '''Neoclassical Transport Model''' is one of the pillars of the physics of magnetically confined plasmas.
	<ref>~~[http://link~~.~~aps~~.~~org/~~doi/10.1103/RevModPhys.48.239 ~~F.L. Hinton and R.D. Hazeltine,~~ Rev. Mod. Phys. '''48''', 239 (1976)]</ref>		<ref>F.L. Hinton and R.D. Hazeltine, [[doi:10.1103/RevModPhys.48.239\|Rev. Mod. Phys. '''48''', 239 (1976)]]</ref>
	<ref>P. Helander and D.J. Sigmar, ''Collisional Transport in Magnetized Plasmas'', Cambridge University Press (2001) ISBN 0521807980</ref>		<ref>P. Helander and D.J. Sigmar, ''Collisional Transport in Magnetized Plasmas'', Cambridge University Press (2001) ISBN 0521807980</ref>
	It provides a model for the transport of particles, momentum, and heat due to Coulomb collisions in confined plasmas in complex magnetic geometries, assuming that the plasma is in a quiescent state.		It provides a model for the transport of particles, momentum, and heat due to Coulomb collisions in confined plasmas in complex magnetic geometries, assuming that the plasma is in a quiescent state.
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	In any case, this "baseline" level facilitates the comparison between devices.		In any case, this "baseline" level facilitates the comparison between devices.
	Neoclassical theory is also used in the process of machine design and optimisation.		Neoclassical theory is also used in the process of machine design and optimisation.
	<ref>~~[http://dx.doi.org/10.1088/0741-3335/50/5/053001~~ M. Hirsch et al. ''Major results from the stellarator Wendelstein 7-AS'', Plasma Phys. Control. Fusion '''50''', 5 (2008) 053001]</ref>		<ref>M. Hirsch et al. ''Major results from the stellarator Wendelstein 7-AS'', [[doi:10.1088/0741-3335/50/5/053001\|Plasma Phys. Control. Fusion '''50''', 5 (2008) 053001]]</ref>

	== Limitations ==		== Limitations ==
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	* A fixed geometry. Neoclassical transport is calculated in a static magnetic geometry. In actual experiments (especially Tokamaks), the magnetic field evolves along with the plasma itself, leading to a modification of net transport. While a slow evolution (with respect to typical transport time scales) should not be problematic, rapid changes (such as magnetic reconnections) are outside of the scope of the theory.		* A fixed geometry. Neoclassical transport is calculated in a static magnetic geometry. In actual experiments (especially Tokamaks), the magnetic field evolves along with the plasma itself, leading to a modification of net transport. While a slow evolution (with respect to typical transport time scales) should not be problematic, rapid changes (such as magnetic reconnections) are outside of the scope of the theory.
	* The linearity of the model. Neoclassical theory is a linear theory in which profiles are computed from sources, boundary conditions, and transport coefficients (that depend linearly on the profiles). No non-linear feedback of the profiles on the transport coefficients is contemplated. However, there are many experimental studies that show that the profiles feed back non-linearly on transport (via [[TJ-II:Turbulence\|turbulence]]), leading to some degree of [[Self-Organised Criticality\|self-organisation]].		* The linearity of the model. Neoclassical theory is a linear theory in which profiles are computed from sources, boundary conditions, and transport coefficients (that depend linearly on the profiles). No non-linear feedback of the profiles on the transport coefficients is contemplated. However, there are many experimental studies that show that the profiles feed back non-linearly on transport (via [[TJ-II:Turbulence\|turbulence]]), leading to some degree of [[Self-Organised Criticality\|self-organisation]].
	* Locality. Neoclassical theory is a theory of diffusion, and therefore it assumes that particle motion between collisions is small with respect to any other relevant spatial scales. This assumption then allows writing down differential equations, expressing the fluxes in terms of ''local'' gradients. This basic assumption is violated under specific conditions, which may include: (a) the low-collisionality limit, (b) any situation in which the gradient scale length is very small (e.g., [[Internal Transport Barrier]]s), (c) locations close to the plasma edge<ref>~~[http://link.aip.org/link/?PHPAEN/8/3305/1~~ T. Fülöp, P. Helander, Phys. Plasmas 8, 3305 (2001)]</ref><ref>~~[http://dx.doi.org/10.1088/0741-3335/47/3/010~~ V. Tribaldos and J. Guasp, ''Neoclassical global flux simulations in stellarators'', Plasma Phys. Control. Fusion '''47''' (2005) 545]</ref>, and (d) particles transported in ''streamers''. Such phenomena could give rise to [[Non-diffusive transport\|super-diffusion]]. Points (a) through (c) can be handled by using a Monte Carlo or Master Equation approach instead of deriving differential equations.		* Locality. Neoclassical theory is a theory of diffusion, and therefore it assumes that particle motion between collisions is small with respect to any other relevant spatial scales. This assumption then allows writing down differential equations, expressing the fluxes in terms of ''local'' gradients. This basic assumption is violated under specific conditions, which may include: (a) the low-collisionality limit, (b) any situation in which the gradient scale length is very small (e.g., [[Internal Transport Barrier]]s), (c) locations close to the plasma edge<ref>T. Fülöp, P. Helander, [[doi:10.1063/1.1372179\|Phys. Plasmas 8, 3305 (2001)]]</ref><ref>V. Tribaldos and J. Guasp, ''Neoclassical global flux simulations in stellarators'', [[doi:10.1088/0741-3335/47/3/010\|Plasma Phys. Control. Fusion '''47''' (2005) 545]]</ref>, and (d) particles transported in ''streamers''. Such phenomena could give rise to [[Non-diffusive transport\|super-diffusion]]. Points (a) through (c) can be handled by using a Monte Carlo or Master Equation approach instead of deriving differential equations.
	* Markovianity. A second assumption underlying diffusive models (including Neoclassics) is Markovianity, implying that the motion of any particle is only determined by its current velocity and position. However, there are situations, such as stochastic magnetic field regions, persistent turbulent eddies, or transport barriers, where this assumption may be violated (due to trapping effects, so that the preceding history of the particle trajectory becomes important). Typically, this would then give rise to [[Non-diffusive transport\|sub-diffusion]].		* Markovianity. A second assumption underlying diffusive models (including Neoclassics) is Markovianity, implying that the motion of any particle is only determined by its current velocity and position. However, there are situations, such as stochastic magnetic field regions, persistent turbulent eddies, or transport barriers, where this assumption may be violated (due to trapping effects, so that the preceding history of the particle trajectory becomes important). Typically, this would then give rise to [[Non-diffusive transport\|sub-diffusion]].

	== References ==		== References ==
	<references />		<references />

Admin: /* Brief summary of the theory */

2011-07-31T09:44:57Z

Brief summary of the theory

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	:<math>		:<math>
	\frac{\partial f_\alpha}{\partial t} + v\cdot \nabla f_\alpha + F \frac{\partial f_\alpha}{\partial v} = C_\alpha(f)		\frac{\partial f_\alpha}{\partial t} + v\cdot \nabla f_\alpha + F \frac{\partial f_\alpha}{\partial v} = C_\alpha(f) + S_\alpha
	</math>		</math>

	where <math>\alpha</math> indicates the particle species, <math>v</math> is the velocity,		where <math>\alpha</math> indicates the particle species, <math>v</math> is the velocity,
	<math>F</math> is a force (the [http://en.wikipedia.org/wiki/Lorentz_force Lorentz force] acting on the particle) and <math>C_\alpha</math> the [[Collision operator\|collision operator]].		<math>F</math> is a force (the [http://en.wikipedia.org/wiki/Lorentz_force Lorentz force], <math>F = q(E + v \times B)</math> acting on the particle), <math>S_\alpha</math> a source and <math>C_\alpha</math> the [[Collision operator\|collision operator]].
	If the chosen collision operator is the Fokker-Planck operator, the equation is called the [http://en.wikipedia.org/wiki/Fokker-planck Fokker-Planck Equation].		If the chosen collision operator is the Fokker-Planck operator, the equation is called the [http://en.wikipedia.org/wiki/Fokker-planck Fokker-Planck Equation].
	The derivation of this collision operator is highly non-trivial and requires making specific assumptions;		The derivation of this collision operator is highly non-trivial and requires making specific assumptions;
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	The collision operator must also satisfy some obvious conservation laws (conservation of particles, momentum, and energy).		The collision operator must also satisfy some obvious conservation laws (conservation of particles, momentum, and energy).

	Once the collision operator is decided, the moments of the Kinetic Equation can be computed. ~~First, some definitions~~ are ~~needed~~:		Once the collision operator is decided, the moments of the Kinetic Equation can be computed.
			These fluid moments are:

	:<math>		:<math>
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	(heat flux)		(heat flux)

			As an example, the evolution equation of the first moment becomes:
			:<math>
			\frac{\partial n}{\partial t} + \nabla \cdot (n u) = S_n
			</math>
			Similar conservation-type equations can be written down for the higher moments.

	The main goal of Neoclassical transport theory is to provide a closed set of equations for the time evolution of these moments, for each particle species. Since the determination of any moment requires knowledge of the next order moment, this requires truncating the set of moments (''closure'' of the set of equations).		The main goal of Neoclassical transport theory is to provide a closed set of equations for the time evolution of these moments, for each particle species. Since the determination of any moment requires knowledge of the next order moment, this requires truncating the set of moments (''closure'' of the set of equations).
	<ref>T.J.M. Boyd and J.J. Sanderson, ''The physics of plasmas'', Cambridge University Press (2003) ISBN 0521459125</ref>		<ref>T.J.M. Boyd and J.J. Sanderson, ''The physics of plasmas'', Cambridge University Press (2003) ISBN 0521459125</ref>

			It is customary to make a number of additional assumptions to facilitate the analysis: e.g., small gyroradius, nested magnetic surfaces, large parallel transport, Maxwellian distribution functions, etc.
			As a consequence of such assumptions, the equations can be restated to reflect the 'radial' transport (normal to the flux surfaces, and averaged over flux surfaces).
			Thus, the magnetic geometry is incorporated at an essential level in the theory.

	The theory takes account of all particle motion associated with toroidal geometry; specifically, ''∇ B'' and curvature drifts, and passing and trapped particles (banana orbits).		The theory takes account of all particle motion associated with toroidal geometry; specifically, ''∇ B'' and curvature drifts, and passing and trapped particles (banana orbits).

Admin: /* Brief summary of the theory */

2011-07-30T12:50:35Z

Brief summary of the theory

← Older revision		Revision as of 14:50, 30 July 2011
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	The collision operator must also satisfy some obvious conservation laws (conservation of particles, momentum, and energy).		The collision operator must also satisfy some obvious conservation laws (conservation of particles, momentum, and energy).

	Once the collision operator is decided, the moments of the ~~Fokker-Planck equation~~ can be computed. First, some definitions are needed:		Once the collision operator is decided, the moments of the Kinetic Equation can be computed. First, some definitions are needed:

	:<math>		:<math>
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	(heat flux)		(heat flux)

	The main goal of Neoclassical transport theory is to provide a closed set of equations for the time evolution of these moments, for each particle species. Since the determination of any moment ~~requieres~~ knowledge of the next order moment, this requires truncating the set of moments (''closure'' of the set of equations).		The main goal of Neoclassical transport theory is to provide a closed set of equations for the time evolution of these moments, for each particle species. Since the determination of any moment requires knowledge of the next order moment, this requires truncating the set of moments (''closure'' of the set of equations).
	<ref>T.J.M. Boyd and J.J. Sanderson, ''The physics of plasmas'', Cambridge University Press (2003) ISBN 0521459125</ref>		<ref>T.J.M. Boyd and J.J. Sanderson, ''The physics of plasmas'', Cambridge University Press (2003) ISBN 0521459125</ref>

Admin: /* Brief summary of the theory */

2011-07-30T12:48:53Z

Brief summary of the theory

← Older revision		Revision as of 14:48, 30 July 2011
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	== Brief summary of the theory ==		== Brief summary of the theory ==

	The theory starts from the ~~(Markovian) [http://en.wikipedia.org/wiki/Fokker-planck Fokker-Planck~~ Equation] for the particle distribution function <math>f_\alpha(x,v,t)</math>:		The theory starts from the Kinetic Equation for the mean particle distribution function <math>f_\alpha(x,v,t)</math>:

	:<math>		:<math>
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	where <math>\alpha</math> indicates the particle species, <math>v</math> is the velocity,		where <math>\alpha</math> indicates the particle species, <math>v</math> is the velocity,
	<math>F</math> is a force (the [http://en.wikipedia.org/wiki/Lorentz_force Lorentz force] acting on the particle) and <math>C_\alpha</math> the ~~Fokker-Planck~~ [[Collision operator\|collision operator]].		<math>F</math> is a force (the [http://en.wikipedia.org/wiki/Lorentz_force Lorentz force] acting on the particle) and <math>C_\alpha</math> the [[Collision operator\|collision operator]].
			If the chosen collision operator is the Fokker-Planck operator, the equation is called the [http://en.wikipedia.org/wiki/Fokker-planck Fokker-Planck Equation].
	The derivation of this collision operator is highly non-trivial and requires making specific assumptions;		The derivation of this collision operator is highly non-trivial and requires making specific assumptions;
	in particular it must be assumed that a single collision has a small random effect on the particle velocity,		in particular it must be assumed that a single collision has a small random effect on the particle velocity,

Admin: /* Brief summary of the theory */

2011-07-30T10:12:45Z

Brief summary of the theory

← Older revision		Revision as of 12:12, 30 July 2011
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	where <math>\alpha</math> indicates the particle species, <math>v</math> is the velocity,		where <math>\alpha</math> indicates the particle species, <math>v</math> is the velocity,
	<math>F</math> is a force (the [http://en.wikipedia.org/wiki/Lorentz_force Lorentz force] acting on the particle) and <math>C_\alpha</math> the Fokker-Planck collision operator.		<math>F</math> is a force (the [http://en.wikipedia.org/wiki/Lorentz_force Lorentz force] acting on the particle) and <math>C_\alpha</math> the Fokker-Planck [[Collision operator\|collision operator]].
	The derivation of this collision operator is highly non-trivial and requires making specific assumptions;		The derivation of this collision operator is highly non-trivial and requires making specific assumptions;
	in particular it must be assumed that a single collision has a small random effect on the particle velocity,		in particular it must be assumed that a single collision has a small random effect on the particle velocity,
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	The theory is valid for all [[Collisionality\|collisionality]] regimes, and includes effects due to resistivity and viscosity. An important prediction of the theory is the [[Bootstrap current\|bootstrap current]].		The theory is valid for all [[Collisionality\|collisionality]] regimes, and includes effects due to resistivity and viscosity. An important prediction of the theory is the [[Bootstrap current\|bootstrap current]].

	~~''(Further detail needed)''~~		== Predictive and interpretative modelling ==

			The derived transport equations can be used in several ways.

			In predictive modelling, the transport is computed on the basis of the magnetic geometry, the collision operator, sources, and boundary conditions. The predicted transport and the resulting profiles can then be compared to experimental data.

			In interpretative modelling, experimentally measured profiles are used to infer the corresponding sources or transport coefficients.

	== Achievements ==		== Achievements ==

Admin at 16:46, 29 July 2011

2011-07-29T16:46:05Z

← Older revision		Revision as of 18:46, 29 July 2011
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	<ref>[http://link.aps.org/doi/10.1103/RevModPhys.48.239 F.L. Hinton and R.D. Hazeltine, Rev. Mod. Phys. '''48''', 239 (1976)]</ref>		<ref>[http://link.aps.org/doi/10.1103/RevModPhys.48.239 F.L. Hinton and R.D. Hazeltine, Rev. Mod. Phys. '''48''', 239 (1976)]</ref>
	<ref>P. Helander and D.J. Sigmar, ''Collisional Transport in Magnetized Plasmas'', Cambridge University Press (2001) ISBN 0521807980</ref>		<ref>P. Helander and D.J. Sigmar, ''Collisional Transport in Magnetized Plasmas'', Cambridge University Press (2001) ISBN 0521807980</ref>
	It provides a model for the transport of particles, momentum, and heat in complex magnetic geometries.		It provides a model for the transport of particles, momentum, and heat due to Coulomb collisions in confined plasmas in complex magnetic geometries, assuming that the plasma is in a quiescent state.
			Thus, transport due to fluctuations lies outside of the scope of the theory.
	The difference between the Neoclassical and the Classical models lies in the incorporation of geometrical effects, which give rise to complex particle orbits and drifts that were ignored in the latter.		The difference between the Neoclassical and the Classical models lies in the incorporation of geometrical effects, which give rise to complex particle orbits and drifts that were ignored in the latter.

174.117.127.205: style

2010-12-14T19:37:32Z

style

← Older revision		Revision as of 21:37, 14 December 2010
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	The Neoclassical Transport Model is one of the pillars of the physics of magnetically confined plasmas.		The '''Neoclassical Transport Model''' is one of the pillars of the physics of magnetically confined plasmas.
	<ref>[http://link.aps.org/doi/10.1103/RevModPhys.48.239 F.L. Hinton and R.D. Hazeltine, Rev. Mod. Phys. '''48''', 239 (1976)]</ref>		<ref>[http://link.aps.org/doi/10.1103/RevModPhys.48.239 F.L. Hinton and R.D. Hazeltine, Rev. Mod. Phys. '''48''', 239 (1976)]</ref>
	<ref>P. Helander and D.J. Sigmar, ''Collisional Transport in Magnetized Plasmas'', Cambridge University Press (2001) ISBN 0521807980</ref>		<ref>P. Helander and D.J. Sigmar, ''Collisional Transport in Magnetized Plasmas'', Cambridge University Press (2001) ISBN 0521807980</ref>