FUSION POWER PLANTS

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UNIVERSITA DI PADOVA CENTRO RICERCHE FUSIONE
FUSION POWER PLANTS Basic Processes and Main
Plant features G. Casini May 2009
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The fusion process

• Nuclear fusion involves the bringing together of
  atomic nuclei. The atom's nucleus consists of
  protons (p) with a single positive charge and
  neutrons (n) of similar mass and no charge. A
  strong nuclear force holds these "nucleons"
  together against the repulsive effect of the
  proton's charge. The same number of negatively
  charged electrons as protons swarm around the
  nucleus to balance the proton charge. The mass of
  the atom lies almost totally in the nucleus.
• The sum of the individual masses of the nucleons
  is greater than the mass of the whole nucleus.
  This means that the combined nucleus is in a
  lower energy state than the nucleons separately.
  The difference, the binding energy (?E?m.c2 ),
  varies from one element to another.
• When two light atomic nuclei are brought
  together to make a heavier one, the binding
  energy of the combined nucleus can be more than
  the sum of the binding energies of the component
  nuclei (i.e. it is in an even lower energy
  state). This energy difference is released in the
  "fusion" process (fusion reaction). See figure
  below)
• A similar situation occurs when heavy nuclei
  split. Again the binding energies of the pieces
  can be more that of the whole and the excess
  energy can be released in the fission process

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Binding energy released in fusion and fission
reactions
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The fusion process in Sun and Stars

• In the Sun and stars a chain of fusion reactions
  occurs which converts hydrogen to helium. There
  are two chains both having the same effective
  results, and which dominates depends on the size
  of the star. For the Sun the proton cycle
  dominates. The overall reaction rate is extremely
  low, but it nevertheless drives the universe due
  to star sizes and huge masses. The particles are
  held together by gravity long enough for
  sufficient reactions to occur. For instance, in
  the core of the Sun the temperatures is 10 - 15
  million C. Along with the extreme pressure (a
  quarter of a trillion atmospheres) and density
  (eight times that of gold), this allows matter to
  be converted into large amounts of energy.

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Making fusion on earth

• To make fusion on a smaller scale on earth, more
  probable reactions have to be used. A figure of
  merit for a reaction is the product of the
  probability of reaction and the energy delivered
  per reaction. (specific reactivity)
• The most attractive fusion reactions are the
  following (see next figure)
• (1), D-T, (2) D-D, and (3) D-3He
• A comparison of them in terms of specific
  reactivity is shown in the following figure.
• D-T is the favorite reaction with a maximum
  reactivity at around 100 million C. The next
  most reactive is DD, about 40 times smaller, and
  D3He, an isotope of helium, about 85 times
  smaller. The DD reactivity value includes "side
  reactions" between D and the DD reaction
  products, namely T and 3He.

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Fusion reactions
Deuterium Tritium 2D 3T g 4He (3,52 MeV)
1n (14,1 MeV)
Deuterium Deuterium 2D 2D g 3He (0,82 MeV)
1n (2,45 MeV) 2D 2D g 3T (1,01 MeV) 1H
(3,02 MeV)
Deuterium Helium 2D 3He g 1H (14,7 MeV)
4He (3,7 MeV)
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Figure of merit for a fusion reaction (reactivity)
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Deuteriom-Tritium fusion reaction
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Plasma power balance

• D and T form a plasma already at few thousand
  degrees.
• The reacting mix of D and T is a plasma at the
  temperatures of tens of million degrees needed to
  obtain adequate fusion reaction cross sections.
• Three main parameters define the operation of a
  plasma in a confinement system
• n plasma density
• ?E confinement time
• T plasma temperature
• ?E E/P quality of plasma thermal insulation
• E thermal energy in the plasma,
• P power needed to maintain the plasma at a
  constant temperature .

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Plasma power balance (1)

• In any isolated system, a power balance can be
  established
• pfus n2 lt?vgtQDT fusion power density
• lt?vgt average cross section-speed product for a
  maxwellian velocity distribution QDT energy
  released in fusion
• Pfus ? pfusdV total fusion power
• P? ?1/5Pfus dV alpha particles power
• Pheat heating power injected in plasma
• Pa Pheat Plosses power balance
• P losses (?3nT dV)/

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Plasma losses

• Breemsstrahlung emitted mainly by the electrons
  of the plasma accelerated by interaction with
  ions. Normally negligeable
• Cyclotron radiation emitted by the electrons
  gyrating in the magnetic field. The power
  associated is, in large measure, absorbed by the
  plasma which is optically thick at these
  frequencies
• Impurity radiation This is the major cause of
  losses. The impurities in the plasma enhance the
  losses by Breemsstrahlung and irradiate energy by
  atomic processes, line radiation and
  recombination, due to high Z impurities, not
  fully ionized at the plasma boundaries. With an
  Fe (atomic Z26), content in the plasma of 0.2,
  10 of fusion power is lost by radiation not
  contributing therefore to heat the plasma
• Conduction and convection they can be reduced
  by shaping, in appropriate way, the magnetic
  field configuration .

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Plasma power balance (2)
At a fixed temperature, plasma ignition is
achieved when Pa Plosses In these
conditions, the D-T reaction is self sustained.
The alpha particles remain confined long enough
within the plasma to transfer their kinetic
energy to other confined nuclei through
collisions, and the energy confinement of the
plasma is sufficiently good so that heating by
these alpha particles can maintain it at the
required burn temperature. In order to achieve
ignition in a 50-50 D-T plasma, a temperature
between 10 and 20 keV is needed. In this range of
temperatures ltsvgt is proportional to T2 and
then ignition condition can be expressed through
the following expression for the triple product
nDTTtE as nDTTtE gt 6x1021 m3 keV s
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Making fusion on Earth (1) Inertial Plasma
confinement

• One approach to achieving the necessary
  conditions for fusion on earth is to exploit the
  inertia (mass) of the particles. Inertial fusion
  involves the firing many times per second of high
  energy particle or laser beams from all
  directions at tiny solid fuel pellets in a
  reaction chamber. Material sputtered off the
  pellet by the high energy beams drives a shock
  wave towards the pellet centre, raising its
  temperature and density. This implosion leads to
  sufficient fusion reactions occurring to overcome
  the losses, and a large amount of energy is
  released in a "micro-explosion". The resulting
  alpha particles, neutrons, and radiation flow
  radially out towards the reaction chamber walls.
  These are situated far enough (typically metres)
  away and built so as to be able to withstand the
  loads.

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Making fusion on Earth (2)Magnetic plasma
confinement

• An alternative approach to achieve fusion in
  earth exploits the charge of the particles. In
  this case the plasma charged particles are
  deflected by a magnetic field and, if the field
  is strong enough, particles will orbit round a
  field line, gradually progressing along it if
  they have some longitudinal velocity..
• The most attractive confinement schemes are
  based on toroidal plasma configurations . But
  unfortunately in a torus the magnetic field gets
  weaker across the minor diameter. Thus the
  particle orbit around the field line is tighter
  on the high field (inboard) side than on the low
  field (outboard) side. The result is a movement
  of the ions upwards and electrons downwards in
  the plasma, and the resulting electric field
  makes the plasma drift radially out of the torus.
  
• To avoid this difficulty various systems have
  been proposed, namely
• - the tokamak
• - the reversed field pinch
• - the stellarator

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The tokamak system

• The present preferred toroidal magnetic
  configuration is named Tokamak.
• This system exploits the fact the plasma, even
  if it is globally neutral, can conduct
  electrical current due to the independently
  moving positively and negatively charged
  particles of which it is composed.
• Then in tokamak a current pulse in a
  transformer primary winding (named central
  solenoid), placed in the hole of the torus,
  creates an electric field and hence drives a
  large current in the plasma ring, which serves as
  the sole secondary winding of the transformer.
  This plasma current provides a component of
  poloidal field in the plasma. In conjunction with
  the toroidal field provided by coils placed
  around the torus, this causes each field line to
  spiral round the plasma torus, generating a
  magnetic surface. Particles orbiting the field
  line are constrained near this surface, unless
  they collide with other particles.

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Tokamak basic configuration

• The tokamak basic configuration involves three
  coil systems producing the following magnetic
  fields, see figure below
• Bt provided by the Toroidal Field (TF) coils.
• B t(R) Btox Ro /R (R torus radius, Bto, Ro
  values on the plasma axis)
• BP, provided by the plasma current I induced
  through the Central
• Solenoid (CS)
• BP(a) m0x I(a) /2p a (a plasma radius)
• Bv provided by Poloidal Field (PF) coils placed
  outside the TF-coils ring

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Tokamak magnetic configuration
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Safety factor (q)

• The combination of toroidal and poloidal magnetic
  field gives
• helical field lines that in a regular situation
  lie on nested magnetic surfaces on which the
  plasma pressure is constant.
• The general pattern of the helical field lines is
  described by the
• safety factor (q )
• q expresses the number of times a field line
  circles the major axis in circling once around
  the minor one
• For magnetic surfaces with circular cross
  section, approximately
• q BT /BP x a/R
• Elementary tokamak theory predicts stability
  against dangerous low order plasma kink modes
  (external kink modes) when
• q(r) gt1 at all radia
• (MHD stability Kruskal-Shafranov criterion )

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Plasma Beta Beta is the ratio between the plasma
average kinetic pressure and the magnetic field
pressure Toroidal beta bT nkT/ BT2/ 2m0
Poloidal beta bP nkT/BP2/2m0 bT bP
1/q2(a)A2  A R/a  For equilibrium reasons
must be bPlt A, then bTlt 1/q2(a)A  If
q(a) 3, A 3 then bT 3.7 For an elongated
D shaped plasma ( b major radius and a minor
radius), taking a fixed q-value, the poloidal
field is increased with elongation since a
magnetic field line must go around a larger minor
conference. Current I scales as b/a and bt as
(b/a)2
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Real magnetic configuration and plasma
instabilities

• The real magnetic configuration of a Tokamak is
  for various reasons more complex ascompared to
  that created only by the TF coils and plasma
  current, namely
• Discrete number of the TF coils across the torus
  
• Presence of the coils for field control
• Presence of coils to divert the magnetic flux
  at the plasma boundry for extraction of unburned
  plasma particles and impurities
• To these factors one has to ad to add the
  macroscopic plasma instabilities which can be
  classified at least according to four categories
• a) External kinks
• b) Internal resistive kinks
• c) Ballooning modes
• d) Disruptive instabilities
• In the assessment of the plasma parameters of a
  power station the capability to avoid these
  instabilities on the plasma confinement is
  assured by fixing un upper limit to bt.,

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Parameters of the main operating tokamaks
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The poloidal magnetic divertor (1)

• A single null poloidal divertor, presently used
  in tokamaks, is the region of the machine between
  the cross point of the magnetic field lines and
  the walls used to exhaust thermal power (good
  part of the power associated with the helium
  ashes) and particles (helium nuclei in particular
  and impurities) (see figure.)
• The cross point, where the two branches of the
  field separatrix intercept, is created by zeroing
  the poloidal field and through it the particles
  and the energy they transport enter the divertor
  region. SOL (scrape- off - flayer) is the region
  of the plasma beyond the separatrix. The region
  of the plasma beyond the separatrix is named SOL
  (scrape-off-layer) SOL is narrow, typically
  less than 10 mm
• Thermal power densities on the divertor plates
  must be kept within the target materials
  temperature and erosion acceptable limits (15-20
  MW7m2)
• High neutral densities must be created in the
  divertor region to facilitate pumping out of the
  vacuum vessel the reaction ashes and the
  impurities

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Magnetic divertor (2)

• Two ways to solve the problem of limiting the
  thermal load on the divertor targets.
• Incline the divertor plates with respect to the
  separatrix in order to distribute the power and
  particles flow on a wider surface (see figure)
• Inject impurities in the plasma edge to increase
  radiation from the scrape-off-layer to first wall
  and reduce the power ending inthe diveror region
• The power deposited in the divertor will be
  10-13 of the total thermal power for conversion
  to electricity, the remaining part being in
  blanket first wall (12-14) in breeding blanket
  (70-75) and few in the shield. The largest
  part of power to divertor will come from
  neutrons, typically (60), the remaining part
  coming from alpha and D-T ions and impurities.

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Single nul poloidal divertor
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Divertor radial cross-section
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Divertor cassette
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The fusion power plant (1)

• (D-T fuel, magnetic confinement, tokamak
  configuration)
• In a fusion power plant the D-T fuel (plasma),
  contained in a vacuum vessel and magnetically
  confined, is heated up to a temperature which
  enables to obtain the number of fusion reactions
  to produce the required power.
• The DT fusion reaction products are neutrons and
  alpha particles
• D T a (3.52 MeV) n (14. 06 MeV)
• Alfa particles (ions) remain confined in the
  plasma volume and deliver , by slowing down,
  their energy to the electrons of the plasma and
  from these to the ions DT, so balancing the lost
  energy of plasma by electro-magnetic radiation
  and heat conduction and convection to the first
  wall.
• Neutrons leave the plasma and by slowing down
  they transfer their energy to the plasma facing
  walls and to a further component named breeding
  blanket and to other more external systems
  (neutron shield, vacuum vessel ,magnets). The
  largest part of heat deposited by neutrons is
  recovered in the plasma facing walls first walls
  and breeding blanket (primary cooling circuit).
• The breeding blanket contains Lithium based
  materials. Neutrons, reacting with its isotopes
  (Li-6 e Li-7), produce tritium which, once
  extracted, is reintroduced in the plasma chamber
  to balance the loss of tritium burnt by fusion
  reactions

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• Fusion power plant (2)
• First wall structures surrounding the plasma must
  face thermo-mechanical and electro-mechanical
  effects as well as the damage due to neutron and
  gamma radiation. This obliges to replace the
  first wall and breeding blanket during the
  lifetime of the plant. A neutron shield is
  placed outside the blanket in order to avoid the
  replacement of vacuum vessel and magnet system
  during the life of the plant.
• The presence of tritium, which is a radioactive
  material, and of materials radiologically
  activated by neutrons, requires remote
  operation for maintenance and for the periodic
  replacements of the internal components of the
  machine.
• The so named ashes from the combustion
  remaining inside the plasma, namely alpha
  particles, unburned D- T ions and impurities
  produced by the plasma-first wall interaction,
  are continuously removed from the vacuum vessel
  by openings in the magnetic field configuration
  (magnetic divertor). The divertor includes a
  target structure (plates) facing the plasma
  where the ions are neutralized and deposit their
  energy and a pumping channel for the exhausted
  gas extraction.

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• Fusion power plant (3)
• Recovered Tritium from plasma exhaust is
  separated from the other elements (Deuterium,
  Protium, impurities) and reintroduced in the
  plasma chamber together with the tritium
  recovered from the breeding blanket (fuel cycle
  system)
• The magnet system consists of various types of
  superconducting coils (Toroidal Field (TF) coils,
  a Central Solenoid (CS) coil and Poloidal Field
  (PF) coils (divertor, stability and correction
  coils). All coils are cooled by a supercritical
  helium flow maintained cryogenic temperature by
  circulation pumps
• The tokamak vessel and superconducting magnets
  are located inside a thermally shielded cryostat
  to maintain the cryogenic temperatures needed for
  superconductivity.

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Layout of a Fusion Power Plant
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Layout of a fusion power station
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Components of a D-T fusion power station

• Plasma and vacuum vessel
• First wall, breeding blanket and neutron
  shielding
• Divertor and plasma exhaust extraction systems
• Magnet and cryogenic systems
• Plasma heating systems
• Heat recovery and electricity conversion sytems
• Tritium and fuel cycle systems
• Control and safety systems
• Remote handling systems for maintenance and
  repair
• Auxiliary power plant systems

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• The design plasma parameters
• Fusion power density ( pfus)
• pfus n2 lt ?v gt e
• for 1 lt T lt 10 keV ? lt ?vgt T2 then
• pfus n2T2
• ?t nT/Bt2/2?o nT 2 ?o ?t / Bt2
• then
• pfus ?t2Bt4
• Limits on bt and Bt are fixed from
  equilibrium/stability and technological reasons,
  respectively

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ltsvgt as a function of T
D T
1
D 3He
2
D D
3
T T
4
T 3He
5
H B
6
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• Selection of plant design parameters
• The selection of the plant parameters implies
  modeling of the interactions among and between
  the plasma physics and technology requirements.
  This leads to a set of equations , as those of
  the plant power and plasma balance, where the
  various terms have a complex dependence on the
  key parameters which determine the plasma,
  engineering and economic performance of a power
  station. Starting from these equations a system
  code has to be set up which enables to evaluate
  in a self consistent manner the parameters of the
  fusion power plant which have to satisfy an
  input requirement, as the minimization of the
  cost of electricity..
• The key parameters for which a limit has been
  identified up to now for plasma performance of
  the plant are
• Energy confinement time tE , (see figure)
• Plasma beta bt , see Fig.
• Plasma density (limit n-Greenwald I/pa2 , but
  no firm basis)
• Safety factor q (q gt 1)
• Neutron wall loading
• Power density at the divertor target
• Toroidal field at the TF conductor

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A simplified model for plasma power balance
evaluation

• Let start by fixing the following parameters
• maximum toroidal field in the superconducting
  coils BTM
• safety factor q (gt1)
• We can write
• I2p /m0 x (a/A) x (BT0 /q) first equation
• BT0 BTM x (R a- dD - dB )/R second equation
• 2/ p ( R-a dB -dC )2 BTRM / 2p R lPL I third
  equation
• Where
• BT0 toroidal magnetic field on the (minor)
  axis
• I plasma current
• dD space between plasma and toroidal coil
  on inner torus side
• dB blanket thickness
• dC thikness of the toroidal field coils
• BTRM transformer core maximum field
• lpl plasma ring inductance
• These last parameters can be evaluated
  separately.
• By solving the system of the three equations we
  can determine
• A (Aspect Ratio), BTO and a ( plasma radius)

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Scaling laws for energy confinement time
8) tE 0.0562 I0.93B0.15n190.41P-0.69R1.97ka0.78e
0.58M0.19
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Limits on ?

• ? Neoclassical tearing modes
• ?t ?N x I/aB (?N beta normalized to
  ideal MHD)
• ? Resistive Wall Modes (coupling to the wall)
• Stabilizing external magnetic fields feedback
  controlled
• ? Alfven Eigenmodes

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Current drive and power station operation
(1) First-generation Tokamaks, operating through
a current generated by an electric field induced
by the transformer (central solenoid) coils
(inductive current drive), are pulsed operation
machines. Future power stations will possibly
operate steady state, with an external power
supply (additional heating ).This power interacts
resonantly with the plasma to create a
super-thermal non Maxwellian particle population
which, when balanced against the background
plasma in momentum space, creates in the plasma
a toroidal current which enables the plasma
current sustainment (non-inductive current
drive). The methods of non inductive current
drive are Neutral beam - Radiofrequency -
Current Drive They are based on the same
technique developed for plasma heating during
start up of the tokamax experimental machines.
These methods offer the way to adjust the plasma
density distribution. Experiments in present
machines have shown the importance to adjust the
current density profile to obtain enhanced
confinement operating regimes and to fight
instabilities.
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• Current drive and power station operation (2)
• An important parameter (Q) which characterizes
  the mode of operation of a power station is the
  ratio of the fusion power (PFus) to the auxiliary
  heating power (PHeat ), named Plasma Gain (Q)
• Q PFus / PHeat
• Ignition (PHeat 0) would correspond to Q
  infinite.
• Power plants will possibly operate steady-state
  with a continuous additional external heating
  power supply without reaching ignition
  conditions. In this case a fraction of the
  electrical power produced by the fusion plant
  will be ricirculated for the auxiliary heating in
  order to create the non inductive plasma current
  operation. This will imply an economic penalty
  as compared to the case of operation at ignition
  conditions, due to the necessity of circulating
  part of the electric fusion power for the
  additional power supply.

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• Bootstrap current and power station operation (3)
• Plasma particles transport in a Tokamak is
  characterized by the presence of trapped
  particles and by their driftt (neoclassical
  diffusion).
• Bootstrap current (BS) is a a self generated
  plasma current parallel to the magnetic field,
  proportional to the plasma ßp i.e. to the plasma
  pressure nT and driven by the plasma pressure
  gradient
• Ibs /Iplasma 0.6 (r/R)0.5 ßp
• Ibs (r) - 1/Bp dp/dr
• BS will be essential in a thermonuclear plasma of
  power plant because the generation of this
  current will allow to reduce the ricirculated
  electric power needed for generating the current
  drive. For this reason at present plasma physics
  efforts are aimed to identify plasma confinement
  regimes at high bootstrap current fraction (ex.
  Reversed Shear regime)
• 80 bootstrap current has been demonstrated in
  JT-60, 70 in JET

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Reactor Power Flow Diagram
PN Pheat/?H Pel PHeat aux. heating power
PN Power to network hH efficiency of aux.
heating power Q plasma gain Pfus/ Pheat Pth
Pth1 Pth2 Pn neutron power Pth1 P?
Pheat 0.2 Q Pheat Pheat Pth2 fb x 0.8
Pfus fb energy multiplication factor of the
blanket Pel (1 0.2 Q 0.8 fb Q) Pheat x
? Ex. Q 30 fb 1.2 Pel 35.8 x Pheat
Recirculated power 20-25
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• References
• http//www.efda.erg/fusion_energy
• R.Andreani (EFDA) The fusion reactor, Master
  Course on Plasma techology and fusion,
  Padova 2006