Fusion Reactor Criteria

1
Fusion Reactor Criteria

• Fusion Power Density
• Power Balance
• Reactor Criteria
• Breakeven and Ignition
• Power Transfer Processes
• Radiation Loss Mechanisms
• Particle Balance and Burn-up Fraction

2
Nuclear Fusion Power Density
Fusion power density
Plasma beta
Then,
Technology of large S.C. coil
Nuclear physics
Plasma physics
where
3
Reaction Parameter, Beta and Cost
4
Comparison between Fusion Reaction Rates
Beam-Maxwellian
T-gtD
D-gtT
DDn
DDp
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Optimization of Fusion Power Density in the
Two-Energy-Component Tokamak Reactor
D.L. Jassby, Nucl. Fusion 15, (1975) 453
Qb
6
Power Balance and Power Gain Ratio
?-particle heating power
Auxiliary heating power per volume
Energy losses
Energy confinement time
Power gain ratio
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Detailed Fusion Reactor Power Balance
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Power Balances
Ion power balance
Electron power balance
by adding
noting that
Define some characteristic temperature and
confinement time
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Criteria for Reactor
Bremsstrahlung (radiation loss)
for maximum reaction rate
fusion power
then
I. Lawson Criterion (? power is directly lost)
II. Ignition (reaction is self-sustained by ?
heating)
II. Zero Net Power (? power is well confined)
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Reactor Criteria and Examples
IV. Hot Ion Mode
? power is well confined
Ions are well confined
Hot ion
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Reactor Criteria
Ideal Breakeven
Fusion power Bremsstrahlung
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Ignition Condition
PAH lt 0
Prad 0
At T30keV,
Q 1 breakeven, Q ? ignition
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Ignition Condition Triple Products
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Approach to Ignition
Constant confinement time
Ignition
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Approach to Ignition Cordey Pass
Trajectory to ignition requiring minimum power
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Stability for Alpha Particle Heating
Constant confinement time
condition for stability at ignition(PAH0)
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Stabilizing Effect from Confinement Degrade
unstable
stable
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Power Transfer Processes
Ideally speaking, we should optimize 1. Ti to
maximize the fusion reaction, and 2. Te to
minimize the power loss.
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Bremsstrahlung Radiation
Radiated power density
summing over all ion species
define
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Syncrotron Radiation
Radiated power for a gyrating electron
radiation damping time
with plasma beta

• Not so serious for DT except
• for the advanced fusion reactor
• with very high Te since
• re-absorption by the plasma
• reduce effective radiative loss rate with
  reflective first wall

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Impurity Radiation

• Assumptions
• A plasma electron excites an available excitable
  electron in an impurity ion via Coulomb collision
• The excitation transfers the thermal energy of
  the impacting electron to the excited electron
• The excited electron quickly radiate and goes
  back to the original unexcited state

Radiated power from impurity
large angle scattering only
? the number of available electrons to be
excited per impurity
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Impurity Radiation
Impurity radiation power
high Z materials are unfavorable
make large by reducing impurity
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Impurity Concentration for Ignition

• Maximum allowable impurity concentration for
  ignition of a D-T plasma as a function of the
  temperature, assuming zero non-radiative losses
• High z material has higher cooling rate
• Low z material has problem of dilution, i.e.
  more particles can be ejected

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Particle Balance and Burn-up Fraction
Ion balance equation
burn-up fraction at Lawson criterion
for steady-state
Burn-up fraction