Laser in Fusion

Department of Electronics of TEI of CreteDr Petridis Kostantinos

LecturerOptoelectronics, Laser and Plasma Technologies Group

Nuclear Fusion

“Since we have tried any energy source in our planet, and since we have burn all the found coal quantities, we have reached the minimum of our energy resources. At the same time we have polluted our environment so much. Now we turn our attention to the star’s energy!!

‘Fusion can give us the energy equivalent of oceans of oil’

Fusion

Fusion • Through fusion we get:

(α) Environmental friendly energy (b) High efficiency source:

The reaction of deuterium with tritium is characterized from a very high efficiency of transformation of mass to energy.

(c) Covers the energy needs of our planet.

• Advantages of laser fusion:

(a) There is no production of CO2

(b) Minimum radioactive products

(c) The fusion fuel exist in vast quantities in sea water and underground.

(d) Each reaction does not demand vast quantities of fuel.

Nuclear Fusion Historical Review

1905: Einstein introduced the famous equation

1920: Francis William Aston discovered the 4 hydrogen isotopes

1920: Arthur Eddington suggested that the Sun produces energy by transforming the

hydrogen nucleus into Helium nucleus accompanied with instantaneous

emission of energy

1939: Hans Bethe introduced the theory concerning the energy production in stars. (Nobel prize 1968).

1930s: The first experiments concerning nuclear fusion took part in Cavendish laboratories in Cambridge University.

1950s: Nuclear fusion experiments in Harwell (UK).

2E mc=

Laser in fusion What is the nuclear fusion?

• The nuclear fusion is the joining together two lighter nuclei in order to generate a

a heavier one.

• During this procedure we have the emission or the absorption of energy.

• The joining of two nuclei with total mass smaller than the iron nucleus leads to

emission of energy whereas the joining of two nuclei with total mass bigger

than this of iron leads to absorption of energy.

• The simplest example of fusion: The fusion between deuterium (2Η – 1

proton and 1 neutron ) and tritium (3Η – 1 proton και 2 neutrons) that generates

Helium 4 and neutrons particles (total emitted energy equal to 17.6 ΜeV of

energy).

Laser in fusionWhat is nuclear fusion?

The nucleus energy is getting higher as bigger the nucleus is. The maximum value that tales is that of iron and nickel. From this point the nucleus energy is getting smaller as the nucleons number increases.

In order the Coulomb repulsion force to be overcome we need energy of the order of 0.01MeV. During the fusion reaction among Deuterium and Tritium the energy that is Released is of the order of 17.6 MeV.

Laser in FusionWhat is nuclear fusion?

Laser in Fusion What is nuclear fusion?

Laser in fusionWhat is nuclear fusion;

• The nuclear fusion is a reaction that takes place in stars of our universe.

• In 1940 the Manhattan project it was the first attempt to apply nuclear

fusion for military purposes. The attempt to apply the nuclear fusion for

peaceful purposes started in 1950s

Laser in FusionWhat is nuclear fusion;

• In order a nuclear fusion to take place the isotopes nuclei should be brought

very close each other. That’s how the Coulomb repulsive forces are going to

be overcome.

• The non-controlled nuclear fusion leads to nuclear explosions.

Application of this is the nuclear bomb.

Laser in fusion What is nuclear fusion?

• The controlled nuclear fusion has a target to produce electrical current and

that’s why 50 years now there is an intense research activity in this field.

• In Tokamak reactors we use magnetic fields in order to bring the nuclei

close enough to initiate the nuclear fusion among the isotopes. Using this

technology it has been achieved the production of energy 10 times more

than the energy that is required to to trigger the fusion reaction.

• The initial heating (10 keV) of the isotopes is necessary in order to overcome

the Coulomb repulsion.

• 1 eV = 11,604 K

Laser in fusionWhat is nuclear fusion?

• The rate f at which the fusion reactions take place depends on the average value of

their cross section σ times the reactants (hydrogen isotopes) velocity times the

reactants density n1 & n2 . Thus:

The multiplication of the cross section of the reactants σ times their velocity increases

as the temperature elevates.

Lawson criterion: The longer the time that the reactants are kept close enough and at

the same time the higher their concentration is, the higher the rate of fusion reaction

is. In order a nuclear fusion to take place the above mentioned product should satisfy

the following condition:

1 2f n n συ=

14 15 310 10 sec/n cmτ = −

Lasers in fusion What is nuclear fusion?

• In order to satisfy the Lawson criterion some temporal confinement

techniques should be applied in order to keep the reactants within

the smallest available volume.

• The temporal confinement techniques are the following:

(a) Gravitational confinement: Takes place in the interior of stars.

(b) Magnetic confinement: Tokamak reactors (n = 1014 cm-3, τ = 1

sec)

(c) Inertial confinement: A pulse of a laser illuminates the fuel and

causes its temperature to elevate under high pressure conditions.

The reactants concentrations are so high that fusion reaction takes

place.. (n = 1025 cm-3, τ = 10-10 sec)

Lasers in fusion What is nuclear fusion?

Laser in Fusion

• The use of lasers in fusion is directly related to inertial confinement scheme.

• The pressure that are developed is of the order of 1012 Atm and the

temperatures that can be reached is of the order of 100 million Kelvins.

• The big target is: The creation of an unlimited energy source.

• The fuel (mixture of deuterium and tritium) is placed within a capsule of a

pill size.

• The inertial confinement demands the symmetrical illumination of the

target. This reduces the energy required for fusion by a factor of 1000.

• The nuclear fusion that involves deuterium and tritium is preferable since it

has the lowest threshold.

Laser in Fusion

Fusion Reactions

Laser in fusion

Laser in Fusion

• The fuel implosion efficiency is close to 10 – 15%.

• During the last phase of implosion the acquired pressure is of the order of 200 Gbars

• The important parameters during the implosion phase are:

(a) The ratio R / ∆R where R is the pellet radius and ∆R is its

thickness. Hydrodynamic instabilities set a limit to the above

ratio. The ratio value is related with the minimum pressure that is

required in order the fusion reaction to take place. Typical values are

located between 25 up to 35. These ratio values correspond to pressures

equal to 100 Mbars and laser intensities of 1018 W / cm2

Lasers in fusion

(b) The convergence ratio defines the ratio of the initial radius RA to the final radius rHS. Typical values for nuclear fusion to take place is of the order of 30 – 40.

• The energy that is released during the nuclear fusion can be estimated using the following relationship:

where εf is the energy per unit mass that is emitted, φ is the reaction efficiency and Μ is the exploded mass.

• Nuclear fusion will take place when:

F fE Mε φ=

14 31.7 10 sec/n cmτ> ×

Τα Laser στην θερµοπυρηνική σύντηξη

• The combination of the confinement and the mass explosion can further increase the exerted pressure to the fuel from 108 Atm to 1012 Atm.

• In order fusion to take part the target – fuel should be illuminated uniformly spatially and temporally.

Laser in fusion

• Target of the nuclear fusion that uses inertial confinement is:

(α) Generation of temperatures in the target area of the order of > 5 keV

(b) The product of density to final radius to be > 0.3 g cm-2.

(c) The generated Helium nuclei through collisions accelerate

Deuterium and Tritium and the whole procedure goes on.

• Through the Lawson criterion is valid that is equivalent to have a high density of reactants for a short time confined with the situation to have a low density reactants for a long time under confinement.

• In the case of laser fusion is attempted the greatest density of reactants. Their confinement time is related to their inertial.

Laser in fusion

• In the case of laser fusion with inertial confinement the following things are valid:

(a) Minimum fuel mass ( deuterium and tritium ) ~ ρ-2 (ρ: density)

(b) Minimum energy of ignition ~ P-2 (P: pressure)

• Requirements:

(a) Few tens of MJ of laser energy to illuminate the target within 10 ns.

(b) The density of fuels should be of the order of 30 g cm-3, the exerted pressure of the order of 120 Gbar, and the fuel mass equals to 1.3 × 10-4 g in the ignition point.

(d) Symmetrical illumination of the target.

• The efficiency of the reaction is almost 100.

Laser in fusion

( )implosion arV P r= ∆

(α) The laser light illuminates the target.

(b) The laser radiation exert a pressure to the fuel target. As

a consequence the target is compressed and at the same

time plasma is created around the target.

(c) The radiation pressure is a function of the laser

radiation intensity and on laser wavelength.

(d) The velocity with which the target is confined is:

(e) The target is confined up to the point where the exerted

pressure takes the value: implosion ablation

rP P Gr

⎛ ⎞⎟⎜= ⎟⎜ ⎟⎜⎝ ⎠∆

Lasers in fusion

(f) The pressure during the confinement has an initial value of the order of 30 Mbar and just before the implosion of the fuel reaches a value of the order of 100 Gbar.

(g) Typical dimensions of the fuel pellet :

(i) Initially: radius 3 mm, thickness 0.5 mm

(ii) finally: radius 0.1 mm (confinement ratio 30:1)

• Theoretical calculations has shown us that the released energy during nuclear fusion depends on the final pellet radius and the final value of the exerted pressure. The greater the final pressure is the lower the energy that the fusion reaction starts.

• The requirements from the laser source are:

(a) Symmetrical illumination of the target.

(b) Laser intensity of 1015 W / cm2 emitted in ultraviolet region.

(c) Use of many laser beams (~ 50).

Lasers in fusion

Lasers in fusion

Lasers in fusion

• There are three different architectures schemes in order to trigger laser fusion:

(α) ‘Direct Drive’ (β) ‘Fast Ignition’ (γ) ‘Indirect Drive’

Lasers in fusion• The ‘direct drive’ scheme (a) is the simplest one. The target is illuminated

symmetrically by hundreds laser beams. This technique is characterized by high gain but also from strong hydrodynamic instabilities that probably will obstruct the achievement of the desired fuel densities in order the fusion to take place.

• The laser beam should deliver its energy to the deuterium and tritium. This means that should penetrate through the generated plasma.

• Laser light can penetrate electron densities smaller than a critical value that is:

• The laser light has in the majority of cases a wavelength equal to 0.35 µm.

( ) ( )21

32

1.1 10cn cm

mλ µ− ×=

Laser in fusion Fast Ignition Scheme

• This technique is less demanded. The compression and the heating of the target are two independent processes.

• The process of compression is similar to ‘direct drive’ set up. The difference is that in fast ignition scheme less of lower power laser beams are used.

• As the target has compressed towards the density that fusion is ready to take place a 2nd petawatt laser beam (pulse duration 10-8 sec) is focused into the plasma and within 10-11

sec are achieved temperatures (high energy electrons are accelerated and collide with the deuterium and tritium) and the nuclear fusion starts.

• This scheme is characterized by the less energy that is needed in order nuclear fusion to start.

• HiPER, OMEGA, FIREX use this scheme

Lasers in fusion Fast Ignition Scheme

Τα Laser στην θερµοπυρηνική σύντηξηFast Ignition Scheme

Lasers in fusionFast Ignition Scheme

Lasers in fusion The HiPER project

• High Power laser Energy Research

• 200 kJ long pulse & 70 kJ short pulse laser beams (CPA lasers)

• Objectives: (α) Clean energy source(b) Unlimited energy source(c) Capability to perform a

high quality research:• Budget : 800 εκατοµµύρια

euros – Complement by 2020

Τα Laser στην θερµοπυρηνική σύντηξηΤο πρόγραµµα HiPER

• The laser that HiPER is going to be used is the PΕTAL and is located in France.

• PETAL: PETawatt Aquitaine Laser (3.5 kJ, pulse duration 0.5 – 5 ps).

Τα Laser στην θερµοπυρηνική σύντηξηΤο πρόγραµµα HiPER

Lasers in fusion The OMEGA EP project

• Location: Rochester, USA.

• Fast ignition scheme.

• Start date: 1995

• 60 laser beams are going to deliver 40000 Joules to a focus point of 1 mmdiameter. This energy is going to be delivered within 1 ns.

Lasers in fusion The FIREX project

• Location: Osaka, Japan• Fast Ignition Scheme • Establishment date: 2003

Lasers in fusion Indirect Drive Scheme

• The technique for laser fusion with the greatest potential is the ‘indirect – drive’.

• This set up will use two of the biggest facilities in the world: (a) National Ignition Facility (NIF) (USA) – (3.5 billions of dollars investment, 1.8 millions of Joules energy).

(b) Laser MegaJoule (LMJ) (France)

• The basic principles of the ‘indirect – drive’ are the same with that one of ‘direct – drive’ one. The only difference is that the fuel is contained in a golden made cylinder.

• The compression of the target is made by the Χrays that are generated (efficiency of 70 – 80%) internally to the cylinder through cylinder illumination by laser beams

Lasers in fusionIndirect drive scheme

Lasers in fusion Fast Ignition Scheme with proton particles

Lasers in fusionFast Ignition Scheme with proton particles

• The ‘indirect drive’ technique is not using the laser beams to trigger the laser fusion.

• We can use charged particles such as protons to suppress the target.

• Advantages:

(a) Steady propagation through the generated plasma.

(b) High efficiency

• Disadvantages: The intensity of the protons beam (beam diameter, pulse duration).

• This technique can be used in ‘direct’ and ‘indirect’ setup.

Lasers in fusion References

• ‘Lasers generate plasma power’, Mike Key, Physics World August 1991, pp 52 – 56

• ‘Laser Compression of Matter to Super High Densities: Thermonuclear Applications’, John Nuckolls et.al., Nature Vol. 239, September 15, 1972, pp 139 – 142.

• ‘Incoherent light on the road to ignition’, C. Labaune, Nature Vol.3, October 2007, pp 680 – 682.

• http://www.hiper-laser.org/• Ενέργεια / ΒΗΜΑ Science Κυριακή 24 Ιουνίου 2007• ΒΒC – Horizon • http://www.lle.rochester.edu• https://lasers.llnl.gov• http://en.wikipedia.org• ‘A high – power laser fusion facility for Europe’, M. Dunne, Nature Physics, Vol.2,

January 2006, pp 2 – 5.• ‘Fast heating of ultrahigh-density plasma as a step towards laser fusion ignition’,

Kodama etal, Nature Vol. 412, 23 August 2001, pp 798-801• ‘Fast heating scalable to laser fusion ignition’, Kodama etal, Nature, Vol. 418, August

2002, pp 933 - 934

Lasers in fusion References

• ‘Fast track to fusion energy’, M. Key, Nature Vol. 412, 23 August 2001, pp 775 – 776.

• “For Nuclear Fusion, Could Two Lasers Be Better Than One?”, M. Schirber, Science Vol. 310, pp1610-11.

• ‘Laser facility flickers into life’, E. Hand, Nature Vol. 457, 29 January 2009, pp. 517

• ‘A new age for science?’, A. Jenkins, Nature Photonics Vol. 2, January 2008, pp. 3 – 5.

• ‘Fast Ignition by Intense Laser – Accelerated Proton Beams’, Roth etal., Physical Review Letters, Vol. 86, Number 3, 15 January 2001, pp 436 – 439.

• ‘Extreme Light’, Gerstner, Nature Vol. 446, 1 March 2007, pp 16 – 18.• ‘NIF wakes up’, Nature Photonics, Vol. 3, April 2009, pp 177.• ‘Η δηµιουργία ενός αστεριού’ Η ΚΑΘΗΜΕΡΙΝΗ, 12 Απριλίου 2009, σελ. 26