Plasma Physics 2
9. Thermonuclear fusion
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Vylepsit …

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Lecture series contents
1.Townsend breakdown theory, Paschen‘s law
2.Glow discharge
3.Electric arc at low and high pressures
4.Magnetized low-pressure plasmas and their role in material deposition methods.
5.Brief introduction to high-frequency discharges
6.Streamer breakdown theory, corona discharge, spark discharge
7.Barrier discharges
8.Leader discharge mechanism, ionization and discharges in planetary atmospherres
9.Discharges in liquids, complex and quantum plasmas
10.Thermonuclear fusion, Lawson criterion, magnetic confinement systems, plasma heating and
intertial confinement fusion.

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Evolution of world‘s primary energy
•meziroční nárůst spotřeby energie v roce 2019:  +7.67E18 J    (celkem 2019: 583.9 EJ – exa Joul)
•meziroční nárůst energie z obnovitelných zdrojů 2019: +3.15 EJ    (celkem 2019: 28.98 EJ)
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Energy consumption by humanity (converted to energy)
•The total consumption from primary energy sources for the year 2019 is 583.9 EJ (exa = 1E18).
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•If we convert this to power for the year and with over 40% efficiency of converting thermal energy
to electricity, we get 7.4 TW (1E12), which is an annual increase of 0.1 TW.
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•For comparison, the power from the Sun hitting Earth is about 40,000 TW, and Earth’s thermal
radiation is about 32 TW.
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•The Temelín power plant has a capacity of 1 GW, meaning that the global energy consumption in 2019
increased by the equivalent of 100 Temelín nuclear power plants.
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•… This is a staggering increase in energy consumption! And of course, thermonuclear fusion is one
of the possible solutions, but why?
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•The difference between the mass of an atom and the sum of the masses of its nucleons is the source
of atomic energy (binding energy), as given by Einstein's equation E = mc2.
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•Deuterium from 1 liter of seawater (0.15 per mille) is energetically equivalent to 300 liters of
gasoline
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olovo
A = 82

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MAIN FUSION PATHWAYS, LAWSON CRITERION, TRIPLE PRODUCT
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Main fusion pathways
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Rate constants of fusion reactions
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•Computed optimal values
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Fuel considerations
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Main fusion pathways
Necessary physical conditions for the synthesis/fusion of light nuclei:
1.Nuclei repel each other, therefore approximately 100 keV is needed for heavy hydrogen isotopes to
come within 1 fm
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2.To achieve these energies/particle speeds, accelerators are very inefficient.
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3.Therefore, it is necessary to heat the matter and use particles from the tail of the Maxwellian
distribution function for speeds (10 keV = 108 K) – hence thermonuclear fusion
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4.Plasma (ionization) is primarily not needed. The fact that the matter at such temperatures will
be in plasma state follows from the Saha equation
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5.Controllability of the reaction:
a)Is it possible to isolate hot plasma? – by gravity (the Sun), inertially (explosions),
electrostatically, and by magnetic fields;
b)How to heat the plasma to such a temperature?
c)How to design a reactor so that its energy balance is positive?
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Lawson criterion
This is a necessary condition for the occurrence of self-sustaining fusion in a thermonuclear
reactor, derived by John D. Lawson in 1955.
It is based on the following reasoning: the power input from nuclear synthesis must be greater than
the loss power, which the plasma loses through various paths (radiation, conduction, etc.).
Therefore:
When considering this equation, it is useful to introduce the concept of confinement time.
This time is necessary for the escape of the entire thermal energy W from the plasma, and
therefore:
Naturally, to obtain quantitative value of the confinement time, we need to know the system as such
and be able to quantify Ploss based on its geometry, volume, etc…
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Lawson criterion – derivation outline
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Assuming thermal quasineutral plasma the total energy is:
Next, we utilize the condition for positive energy balance of the fusion reaction
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Finally, we arrive at the Lawson criterion
Which for the D-T system gives:
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kinetic energy of charged particles
number of reactions per unit time
(reaction frequency)
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Triple product

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Lawson parameter

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Fusion devices built to date

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FUSION SETUPS
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Fusion setups

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FUSION SETUPS – PINCHES
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Fusion in pinch systems
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In z-pinch and theta-pinch systems (see arc lecture), plasma density can be high enough to observe
measurable fusion in H2 plasmas.
As you can imagine, Q factor here is nearly zero, good for research purposes only.

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FUSION SETUPS – MAGNETIC CONFINEMENT FUSION (MCF)
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Drifts in B fields
Summary of charged particle drifts you should already know
•grad B drift, caused by a change in the density of magnetic field lines, the force is directly
proportional to grad B
•drift caused by a general force and gravitational drift, perpendicular to the gravitational and
magnetic field
•drift caused by the curvature of the B field lines, centrifugal force
•polarization drift, caused by a slow change in the electric field over time, induced force
•ExB drift

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Drifts in B fields
•Curvature drift is a consequence of centrifugal force due to varying B field strength
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•Practically, when you curve magnetic field (e.g. from a solenoid), the magnitude goes down
as well, so there is gradB field.
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•As a consequence, in toroidal B fields, particles always escape via the torus OD
because there is always a gradient B there.

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Isolation through B field
•The condition for the balance between the kinetic pressure of the plasma and the magnetic pressure
Pm​ of the external confinement field, the volumetric density of electromagnetic energy:
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•However, magnetic confinement systems have a limited mechanical strength at ca p=10 Mpa
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•For a temperature T=200 MK gives a fuel concentration at the level of 10 Pa, or a density of
2.1021 m−3
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•According to the Lawson's criterion, this gives a confinement time of 0.1 s for D-T or 10 s for
D-D.
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•At the same time, this also means that a magnetic thermonuclear reactor must be constructed as a
vacuum vessel, which implicitly ensures resistance to accidents that would disrupt the vacuum and
thus automatically stop the reaction.
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Isolation through B field
The energy production scheme could then look as follows:
1.A fusion reactor mixes D (deuterium) and T (tritium) isotopes at the center of the reactor and
the heat from the released neutrons is captured by a mantle of molten Li (lithium).
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2.This heat then generates steam in a heat exchanger, which will drive a turbine that delivers
electrical energy to the grid.
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3.Meanwhile, lithium reacts with slow neutrons to produce T (tritium), which can be used as new
fuel.
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4.The charged alpha particles (He) can be used for direct electricity production through so-called
magnetohydrodynamic (MHD) generators.
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Magnetic confinement fusion - Tokamak
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Magnetic confinement fusion - Tokamak
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Magnetic confinement fusion - Stellarator
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Highly tailored B field reduces gradB drift lossess

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Magnetic confinement fusion - Stellarator
Wendelstein-7X in Greifswald is a very succesful testbed for high power levels (even though
steady-state demonstrations done with He, no fuel)
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FUSION SETUPS – INERTIAL CONFINEMENT FUSION (ICF)
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Inertial confinement fusion
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Inertial confinement fusion – direct vs indirect drive
Scientists create effective 'spark plug' for direct-drive inertial confinement fusion experiments

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FUSION SETUPS – INERTIAL ELECTROSTATIC CONFINEMENT (IEC)
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Inertial electrostatic confinement
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TAKE AWAYS
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Take aways
•Main fusion reactions, optimum in the cross section.
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•Lawson criterion and parameter, triple product.
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•Different fusion setups with emphasis on MCF as the most widespread concept.