HSB, SU2001, 17.9.01 Max-Planck Institut für Plasmaphysik Introduction to

Plasmaphysik,
IPP-Euratom Association, D-85748 Garching
 Fusion in the stars
 Fusion research

on earth
- Inertial Confinement Fusion
- Magnetic Confinement Fusion (MCF)
 Prospects for a fusion reactor

IPP Summer University on Plasma Physics, Garching, Germany, 17-21 September 2001

compared to single
nucleons: E = m•c



Energy gain possible from
- fission of heavy nuclei or
- fusion of light nuclei.

 Fusion has advantages:
+ fuel resources
+ safety considerations
+ waste production.

Similiar to chemistry, also nuclear reactions set free the binding energy:
For nuclei, however, it is MeV, not eV as for the electrons binding molecules.

(strong
interaction) is active only for

distances in the order of the
nucleus dimensions (fm).

 For larger distances, the
repulsive Coulomb force
dominates 
Potential wall: some 100 keV,
impossible to overcome!


 1928, Gamov explains -decay with quantum mechanics:
spatially decaying wave has a finite value for r < r n,
 finite probability for tunneling through the Coulomb wall:
Ptunnel  exp{-2 Z1Z2e2/h v}
 Highest reaction probability for light nuclei at high relative velocity!

The sun produces
continously energy, with a

total power of 3.6•1017 GW.

 In doing so, it converts per
second 600 Mio. tons of
hydrogen into 596 Mio. tons
of helium.

 The power flux arriving on
earth is 1.4 kW/m2
(above the atmosphere,
without absoprtion).

NASA, Skylab space station December 19, 1973, solar flare reaching 588 000 km off solar surface

involves the
weak interaction, trans-
forming a

proton into a
neutron, resulting in a
very long time scale,
i.e. small reaction rates.
 This is the reason for the
long life time of stars.


 The neutrinos from this reaction are the only particles to be observed
 An alternative to this first step involves 3 body collisions, and is
therefore very rare: p + p + e-  d + e
 Fusion reactions also create the heavier nuclei in the stars
 stellar Nucleosynthesis

of neutrinos
in a chlorine detector (Davis,

Homestake gold mine, South
Dakota, 1964) found only
~ 30% of the expected neutrino flux.
Sensitive only to neutrinos above
814 keV: 37Cl+ e  37Ar + e-
 Measurements with a Cerenkov
detector (700 tons H2O, Kamiokande,
1989) saw ~ 44% of the expected
neutrinos.

 Only in 1992 (GALLEX, Gran Sasso and SAGE, Caucasus), the low energy
neutrinos could be observed: 37Ga + e  37Ge + e-
 These experiments found 50% and 58%, respectively, of the expected flux.
 Solar modell? or Neutrino oscillations?
First indications of oscillations in Super-Kamiokande, 1998.

Hans Bethe (Cornell University) and
Carl-Friedrich von Weiysäcker.



Catalytic process at temperatures
above 1.5 keV, based on 12C.

 Not important in the sun, but for
all larger (i.e. hotter) stars.


 Net reaction:
4 p  4He + 2 e+ + 2  + 3 

fusion reactions!
7
 The weak interaction makes the
pp-chain

a rather slow reaction.

=> long lifetime of stars.

 The huge mass of the sun makes
up for that easily, still resulting in
a large power production.

 However, for power production on
earth, the weak interaction has to
be avoided.

 For the small volume we can afford,
we need faster fusion reactions.

3H,
the heavy hydrogen isotopes.

 The reaction energy is

distributed
to the reaction products inversely
to their mass ratio (energy and
momentum conservation).

 Best choice: the DT-reaction

D + D  3He + n + 3.27 MeV (50%)
or T + p + 4.03 MeV (50%)
D + T  4He + n + 17.59 MeV
D + 3He  4He + p + 18.35 MeV

can be written as

 = S(E) • 1/E • exp{-BG/E}
Tunneling

probability,
BG is the Gamov constant

9

Quantum mechanical
geometry factor

Erel [keV]

Astrophysical S-function,
describes the nuclear
physics of the reaction

of 3.3•10-5 in water
 static range of

billions of years.

 Tritium is a radioactive isotope and decays with a half life of 12.33 years:
T  He + e- + e
 no natural tritium available, but production with fusion produced
neutrons is possible:
n + 6Li  4He + T + 4.8 MeV

n + 7Li  4He + T + n‘ - 2.5 MeV
The latter reaction allows self-sufficient tritium breeding.

 Lithium is very abundant and widespread (in the earth‘s crust and
in the ocean water), sufficient for at least 30 0000 years.

is necessary  accelerator?
No! Coulomb scattering makes the beams diverge

 not efficient

Thermalised mixture of deuterium
and tritium at temperatures of
some 10 keV is necessary  plasma.

Energy distribution of particles in a
thermal plasma: Maxwell distribution

f(v) = (m/2kT)3/2 • exp(-mv2/2kT)



where f(v) is the number of particles
in the velocity interval [v, v+dv].

n1 • n2 •
when is

the average of  •v over the velocity
distribution, and v is the relative velocity
 Transforming the equation into the center-of-mass
sytem yields

< •v>  (Er) • Er • exp(-Er/kT)


when Er is the rel. kinetic energy
and mr is the reduced mass,
1/mr = 1/m1 + 1/m2 .

The fusion power

equals the loss by radiation,

(when c1

= 5.4•10-37 Wm3keV-1/2, and Zeff = niZi2/n is the effective plasma charge),
and by transport (diffusion, convection,
Charge-Exchange):

With nD= nT= n/2, Ti =Te =T we find a condition for the fusion product nT:




Ignition: The neutrons leave the plasma, the -particles are confined and
heat it. Only their energy should enter the balance! Efus  E

C
additional
The -particles also dilute the plasma, as they
are intrinsically coupled

to fusion power
(3.53•1011 atoms/s/W).
 For steady state operation, power and
particle balances have to be solved together.
 Closed curves parametrized by the normal.
He-confinement time He = *He/ E

inrease the
radiation losses from bremsstrahlung,


 but they

also dilute the plasma,
thereby decreasing the fusion power.


 This results in a maximum allowable
concentration, which depends strongly
on the charge of the respective impurity.

Magnetic confinement: A thermal plasma is confined by magnetic fields

and heated to high temperature.

2) Inertial confinement: A small
frozen fuel pellet is heated and
compressed symmetrically by
high power beams: Ignition
and burn while ist „inertia“
keeps it together.
- Ignition in a small, central spot
(low n), propagating outward
into area of high n (low T), spark
ignition (Nuckolls et al. 1972)

- Problems: - Uniformity of irradiation and compression,
- Rayleigh-Taylor-Instabilities
- Drivers

essential to prevent growth of
Rayleigh-Taylor instabilities.

1) High requirement for

surface finish of fuel capsules,
r/r < 0.08 m/1.11 mm = 7•10-8 (NIF-Design).

2) With direct drive, irradiation with many beams and high spatial
homogeneity of the beam profile is neccessary.

A lot of techniques have been developed, and absorption
inhomogeneities of about 3% rms have been achieved
(GEKKO, 1996).

3) Alternatively: Hohlraum

Heavy ion driven
hohlraum target for ICF.
This simulation shows the build

up in time of the radiation
temperature from 5e5K (blue)
to 3e6 K (red) inside the outer
casing.

Lower figure: Rayleigh-Taylor-
Instability during ignition and
burn of an ICF target imploded
by a non-uniform pressure pulse.
This simulation shows the density
(l) and temperature (r).
Blue and red colors are low and
high values respectively.

of a high-Z
hohlraum, which then emits thermal
radiation (X-rays), which

is absorbed
with high efficiency.

Uniformity of the target irradiation can
be achieved in so-called Hohlraums:

Lindl et al.
Phys. Plasmas, 1995

10 ns
Repetition rate: 1-10 Hz
Energy gain should be larger

than 1000

LASER:
1) Neodym glass laser: at = 1.06 m, pellet too small.
Improvement by frequency conversion to 530 nm (70%) or 350 nm (50%).
driver < 1%, repetition rate about 1 pulse/2 hrs.
GEKKO XII, Osaka 25 kJ in 1 ns, 12 beams
NOVA, Livermore 125 kJ in 1 ns, 10 beams
Pumping presently by flashlamps (white light)  Solid State Diode Pumped
Lasers (Yb:S-FAP crystals) with efficiencies up to 20% under development
(LLNL, 1998: 1 J).

2) KrF gas laser: = 248 nm
driver ~ 1%, potenial for development, AURORA, Los Alamos: 10 kJ in 500 ns.

kJ at 350 nm.
Target chamber 
( 4.6m Al, 13 cm

thick)




 Laser bay
(each frame contains 5
laser chains, 137 m long)

absorption:
light ions: 10 MeV, requiring ~ 10 MA,
heavy ions: 10 GeV

~ 10 kA (Pb)

A) Light ions: high currents produced in
Pulsed Power Diodes, PBFAII, Sandia:
2 MJ in 20 ns, high efficiency, problems
with - arcing
- focussing and beam transport
- energy spread,
- repetition rate.

B) Heavy ions: Induction Linacs or RF Linacs with storage rings
- high efficiency (25% has been achieved)
- high repetition rate (3 Hz, GSI Darmstadt)
- good beam transport
- and focussing (using plasma lenses)
GSI Darmstadt: 500 J in 50 ns, I20+ 300 MeV/amu.

Bock
Phys. Bl. 37 (1981) 214

they generate strong X-Rays during the collapse,
- mult-wire arrays are

more stable, generate
even more X-Rays!

lasers (in two stages),
- frequency-tripled Nd glass
laser at

350 nm,
- with an output of 500 TW,
- and 1.8 MJ energy on the target,

for defense applications and inertial fusion
ignition (explore ignition with both indirect-drive
and direct-drive targets).

Lindl et al.,
Phys. Plasmas, 1995

is designed
to absorp 135 kJ,
and to yield 15 MJ

 gain = 110.

years delay)
with 96 lasers.

chamber

perpendicular to B only from
collisions. Particles escape only parallell
to B,

i.e. at the ends.
 bend it to a torus.

a radial gradient, B ~ 1/R


 centrifugal force and gradient

drift separate electrons and ions:




 charge separation creates electric field,
which in turn results in an ExB-drift



 The magnetic field lines have to be twisted, so that
they „average“ over regions with strong and weak field.

lines.

Invented in the 50‘s by
L. Spitzer jr. At Princeton.

+

Only external currents,
+ well controllable,
+ can be run stationary,

- problem of nested coils,
- trapped particles unconfinde

 need and potential for
optimization
 modular stellarators

1996,
av. Minor radius: 0.53 m start of construction: summer 1997,
Magnetic field: 3

T, superconducting order of coils in December 1998,
Diameter of machine: 15 m, height: 4 m start of operation: 2006.

plasma as secondary
winding of a transformer.

Invented in the 50‘s in

Moscow,
by L. Artsimovich and Sacharov.

+ Intrinsic heating,
- due dur the transformer
instationary  current drive
- possibility of current disruptions
+ most advanced fusion concept

= 1.6
Bt  3.5 T Ip  1.4 MA PH 

28 MW

start of operation in 1991

surfaces, but
 plasma edge has to be defined either

- physically by a material limiter, or
- magnetically by additional poloidal
fields, defining a last closed flux
surface, the separatrix.

 First successful experiments inASDEX:
- cleaner plasmas
- steep edge gradients
 H-mode with improved confinement

 Meanwhile all major tokamaks use a
divertor for power and particle exhaust.

 Stellarators have an intrinsic separatrix

the separatrix,
some eV,  H

steep gradients at
the separatrix

strong radiation in

the
divertor

= 1.25 m  = 1.6
Bt  3.5

T Ip  7.0 MA PH  30 MW
start of operation in 1983

records in JET:

Pfusion = 16 MW

Q = 0.65

are close to breakeven,

 The next step (ITER) will

ignite ot at least operate
at high Q (10),

 and thereby prove the scientific
and technological feasibility
of fusion energy.

Europe, Japan, Russia,
and the USA

(before 1998).

 Outline Design in 1999,
Final Report due
July 2001.

12 m

R [m] 6.2
a [m] 2.0
k 1.7
d 0.35
Ip [MA] 15.1
B [T] 5.3
Tpuls [s] 400
Pfusion [MW] 400

have been built
in the R&D

- to prove the technologies
-

to get a reliable costing

CANADA