Physics:Quantum Lawson criterion - Revision history

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	~~{{Quantum article nav\|previous=Physics:Quantum magnetic confinement\|previous label=Magnetic confinement\|next=Physics:Quantum Quark–gluon plasma\|next label=Quark–gluon plasma}}~~



	{{Short description\|Criterion for igniting a nuclear fusion chain reaction}}		{{Short description\|Criterion for igniting a nuclear fusion chain reaction}}
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	{{Short description\|Criterion for igniting a nuclear fusion chain reaction}}I		{{Short description\|Criterion for igniting a nuclear fusion chain reaction}}

	{{Quantum matter backlink\|Plasma and fusion physics}}		{{Quantum matter backlink\|Plasma and fusion physics}}

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	{{Short description\|Criterion for igniting a nuclear fusion chain reaction}}~~Book II~~		{{Short description\|Criterion for igniting a nuclear fusion chain reaction}}I

	{{Quantum matter backlink\|Plasma and fusion physics}}		{{Quantum matter backlink\|Plasma and fusion physics}}

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	{{Short description\|Criterion for igniting a nuclear fusion chain reaction}}		{{Short description\|Criterion for igniting a nuclear fusion chain reaction}}Book II

	{{Quantum matter backlink\|Plasma and fusion physics}}		{{Quantum matter backlink\|Plasma and fusion physics}}

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	{{Short description\|Criterion for igniting a nuclear fusion chain reaction}}		{{Short description\|Criterion for igniting a nuclear fusion chain reaction}}

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	<div style="flex:1; line-height:1.45; color:#006b45; column-count:2; column-gap:32px; column-rule:1px solid #b8d8c8;">		<div style="flex:1; line-height:1.45; color:#006b45; column-count:2; column-gap:32px; column-rule:1px solid #b8d8c8;">
	The '''Lawson criterion''' is a [[figure of merit]] used in [[Physics:Quantum Fusion\|nuclear fusion]] research. It compares the rate of energy generated by fusion reactions within fusion fuel to the rate of energy losses from the plasma environment. When the rate of energy production exceeds the rate of energy loss, the fusion system can produce net energy. If enough of this energy is retained within the plasma to sustain further reactions, the plasma reaches [[Physics:Quantum Fusion#Ignition\|ignition]].<ref name="Lawson"/>		The '''Lawson criterion''' is a figure of merit used in [[Physics:Quantum Fusion\|nuclear fusion]] research. It compares the rate of energy generated by fusion reactions within fusion fuel to the rate of energy losses from the plasma environment. When the rate of energy production exceeds the rate of energy loss, the fusion system can produce net energy. If enough of this energy is retained within the plasma to sustain further reactions, the plasma reaches [[Physics:Quantum Fusion#Ignition\|ignition]].<ref name="Lawson"/>

	The concept was first developed by [[John D. Lawson ~~(scientist)\|John D. Lawson]]~~ in a classified 1955 report at the Atomic Energy Research Establishment in Harwell, United Kingdom.<ref>~~{{cite tech report~~		The concept was first developed by John D. Lawson in a classified 1955 report at the Atomic Energy Research Establishment in Harwell, United Kingdom.<ref>{{Dead link\|date=November 2023}}</ref> The work was later declassified and formally published in 1957.<ref name="Lawson">{{Cite journal
	~~\|last=Lawson~~
	~~\|first=J. D.~~
	~~\|title=Some criteria for a useful thermonuclear reactor~~
	~~\|date=December 1955~~
	~~\|issue=A.E.R.E. GP/R 1807~~
	~~\|institution=Atomic Energy Research Establishment, Harwell, Berkshire, U. K.~~
	\|url=[https://www.euro-fusion.org/fileadmin/user_upload/Archive/wp-content/uploads/2012/10/dec05-aere-gpr1807.pdf](https://www.euro-fusion.org/fileadmin/user_upload/Archive/wp-content/uploads/2012/10/dec05-aere-gpr1807.pdf)
	}}{{Dead link\|date=November 2023}}</ref> The work was later declassified and formally published in 1957.<ref name="Lawson">{{Cite journal
	\|last=Lawson		\|last=Lawson
	\|first=J. D.		\|first=J. D.
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	As originally formulated, the Lawson criterion defines a minimum value for the product of plasma density and energy confinement time required to obtain net fusion power. Later refinements introduced the more useful '''fusion triple product''', which combines plasma density, temperature, and confinement time into a single performance measure.<ref name="Lawson"/>		As originally formulated, the Lawson criterion defines a minimum value for the product of plasma density and energy confinement time required to obtain net fusion power. Later refinements introduced the more useful '''fusion triple product''', which combines plasma density, temperature, and confinement time into a single performance measure.<ref name="Lawson"/>

	On 8 August 2021, researchers at the [[National Ignition Facility]] at [[Lawrence Livermore National Laboratory]] announced an inertial confinement fusion experiment that exceeded the Lawson criterion for ignition conditions.<ref>{{cite web		On 8 August 2021, researchers at the National Ignition Facility at Lawrence Livermore National Laboratory announced an inertial confinement fusion experiment that exceeded the Lawson criterion for ignition conditions.<ref>{{cite web
	\|url=[https://www.sciencealert.com/scientists-achieved-self-sustaining-nuclear-fusion-but-now-they-cant-replicate-it](https://www.sciencealert.com/scientists-achieved-self-sustaining-nuclear-fusion-but-now-they-cant-replicate-it)		\|url=[https://www.sciencealert.com/scientists-achieved-self-sustaining-nuclear-fusion-but-now-they-cant-replicate-it](https://www.sciencealert.com/scientists-achieved-self-sustaining-nuclear-fusion-but-now-they-cant-replicate-it)
	\|title=Scientists Achieved Self-Sustaining Nuclear Fusion… But Now They Can't Replicate It		\|title=Scientists Achieved Self-Sustaining Nuclear Fusion… But Now They Can't Replicate It
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	#'''Fusion''' is the energy generated by nuclear fusion reactions.		#'''Fusion''' is the energy generated by nuclear fusion reactions.
	#'''Radiation loss''' is the energy lost through electromagnetic radiation such as [[X-rays]].		#'''Radiation loss''' is the energy lost through electromagnetic radiation such as X-rays.
	#'''Conduction loss''' is the energy carried away by escaping plasma particles.		#'''Conduction loss''' is the energy carried away by escaping plasma particles.
	#'''Efficiency''' measures how effectively the reactor converts fusion energy into useful power.		#'''Efficiency''' measures how effectively the reactor converts fusion energy into useful power.

	Lawson estimated the fusion power using a thermalized plasma obeying a [[Maxwell–Boltzmann distribution]].<ref name="autogenerated1963">{{Cite journal		Lawson estimated the fusion power using a thermalized plasma obeying a Maxwell–Boltzmann distribution.<ref name="autogenerated1963">{{Cite journal
	\|last1=Spitzer		\|last1=Spitzer
	\|first1=Lyman		\|first1=Lyman
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	* <math>n_A</math> and <math>n_B</math> are the number densities of the fusion fuels,		* <math>n_A</math> and <math>n_B</math> are the number densities of the fusion fuels,
	* <math>\sigma</math> is the fusion ~~[[Cross section (physics)\|~~cross section]],		* <math>\sigma</math> is the fusion cross section,
	* <math>v</math> is the relative particle velocity,		* <math>v</math> is the relative particle velocity,
	* <math>E</math> is the fusion energy released per reaction.		* <math>E</math> is the fusion energy released per reaction.
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	By balancing fusion power against radiation losses, Lawson estimated minimum ignition temperatures of approximately:		By balancing fusion power against radiation losses, Lawson estimated minimum ignition temperatures of approximately:

	* 30 million K (2.6 keV) for the [[deuterium]]~~–[[tritium]]~~ reaction,		* 30 million K (2.6 keV) for the [[Physics:Quantum deuteron\|deuterium]]–tritium reaction,
	* 150 million K (12.9 keV) for the deuterium–deuterium reaction.<ref name="Lawson"/><ref>{{Cite web		* 150 million K (12.9 keV) for the deuterium–deuterium reaction.<ref name="Lawson"/><ref>{{Cite web
	\|title=Energy Converter		\|title=Energy Converter
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	}}</ref>		}}</ref>

	Major fusion experiments such as [[JT-60]], [[TFTR]], [[JET]], and [[ITER]] are often evaluated using the triple-product diagram shown above.<ref>{{cite web		Major fusion experiments such as JT-60, TFTR, JET, and ITER are often evaluated using the triple-product diagram shown above.<ref>{{cite web
	\|url=[http://www-jt60.naka.jaea.go.jp/english/html/exp_rep/rep36.html](http://www-jt60.naka.jaea.go.jp/english/html/exp_rep/rep36.html)		\|url=[http://www-jt60.naka.jaea.go.jp/english/html/exp_rep/rep36.html](http://www-jt60.naka.jaea.go.jp/english/html/exp_rep/rep36.html)
	\|title=World Highest Fusion Triple Product Marked in High-βp H-mode Plasmas		\|title=World Highest Fusion Triple Product Marked in High-βp H-mode Plasmas
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	== Inertial confinement ==		== Inertial confinement ==

	The Lawson criterion also applies to [[Physics:Quantum Magnetic confinement fusion\|magnetic confinement fusion]] and [[inertial confinement fusion]]. In inertial confinement systems, confinement time is determined by the expansion time of the compressed fuel pellet.		The Lawson criterion also applies to [[Physics:Quantum Magnetic confinement fusion\|magnetic confinement fusion]] and inertial confinement fusion. In inertial confinement systems, confinement time is determined by the expansion time of the compressed fuel pellet.

	For inertial confinement fusion, the criterion is often written as:		For inertial confinement fusion, the criterion is often written as:
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	== Non-thermal systems ==		== Non-thermal systems ==

	The Lawson criterion was originally derived for thermalized plasmas, but some fusion concepts use non-thermal particle distributions. Examples include the [[fusor]], [[polywell]], and [[migma]] concepts.		The Lawson criterion was originally derived for thermalized plasmas, but some fusion concepts use non-thermal particle distributions. Examples include the fusor, polywell, and migma concepts.

	In such systems, energy losses from radiation and particle conduction remain major obstacles to net energy production.<ref>{{Cite journal		In such systems, energy losses from radiation and particle conduction remain major obstacles to net energy production.<ref>{{Cite journal

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	{{Quantum article nav\|previous=Physics:Quantum magnetic confinement\|previous label=Magnetic confinement\|next=Physics:Quantum Quark–gluon plasma\|next label=Quark–gluon plasma}}		{{Quantum article nav\|previous=Physics:Quantum magnetic confinement\|previous label=Magnetic confinement\|next=Physics:Quantum Quark–gluon plasma\|next label=Quark–gluon plasma}}



	{{Short description\|Criterion for igniting a nuclear fusion chain reaction}}		{{Short description\|Criterion for igniting a nuclear fusion chain reaction}}Book II

	{{Quantum matter backlink\|Plasma and fusion physics}}		{{Quantum matter backlink\|Plasma and fusion physics}}