NUCLEAR

FUSION

3 simple questions:

• why does the sun shine ?

• why is gold more expensive than iron ? much rarer

• what is radioactivity ?

3 chapters

• basic physics of nuclear fusion

• nuclear fusion in stars

• nuclear fusion as energy supply on earth ?

basic physics

of

nuclear fusion

of elements

atomism

explains chemistry: 92 elements (from H to U)

increasing weight, regularities in properties (alkalines, halogenes,

noble gases, ...)

all of them found in nature ! WHY ?

job for the physicists

heat up pure elements --> emission of light in characteristic colours „spectra“

all explained by quantum mechanics :

atoms are not fundamental but composed of a small nucleus 10-15 m

and a cloud of electrons 10-10 m

the electrons are negatively charged, the nuclei positively,cloud and nucleus are held together by the electromagnetic force

analogy: electron cloud the size of a football stadium 100 m --> size of football (nucleus) at the centre point: 1 mm

nuclear physics

H (lightest nucleus) has 1 electron and 1 positively charged particle as nucleus = proton

2 problems for heavier nuclei:- how can many protons stay together at such small distances ? (repulsion of equal electric charges !)

- nuclei with charge Z have a mass mZ ≥ 2Z mp

possible explanation: need another neutral particle with mn ≈ mp

and a special force between n and p

neutron postulated 1920, experimentally proven 1932 (Chadwick)

new force: strong interaction

--> with p and n and strong int. nuclei can be built up

„rules of the game“ for building up nuclei out of p and n :

• quantum mechanics • special relativity • weak interactions

quantum mechanics :

p and n have spin 1/2 (fermions) no 2 fermions can be in the same state additional p and n are less tightly bound --> „shell structure“

Epot

n p

special relativity : E = m.c2

combination of a and b to system S --> mS < ma + mb

„mass defect“ ∆m = mS - (ma + mb)

energy liberated = ∆ m.c2 = „binding energy“

weak interaction : p + e- <--> n + e

n.b. also need to explain why some nuclei send out various types of radiation

„radioactivity“

„construction on paper“ of nuclei

assume unlimited availability of p and n in either spin state (up or down )

notation: AZ , e.g. hydrogene = 1H

2 nuclei: pp, nn, or pn

S.I. is stronger for parallel spins not allowed for identical particles --> only pn bind !

= deuteron (p n + p n ) = 2H

3 nuclei: ppp and nnn don‘t bind,

pnn OK = triton = 3H

ppn OK = 3He

Epot

n p

4 nuclei: pppn and pnnn don‘t bind

p p n n jackpot !

= 4He

all 4 nuclei in ground state total spin = 0 very high binding energy

= particle

5 nuclei: all unstable

6 nuclei: 3p3n OK = 6Li (= )

7 nuclei: 4p3n unstable

3p4n OK = 7Li

8 nuclei: 4p4n unstable (=

Epot

n p

Epot

n p

Epot

n p

transition with radiation of high energetic photon

- radiation

+

Epot

n p

Epot

n p

transition with transmutation of p into n

- radiation

with emission ofpositron and neutrino

p n + e++ e

(also n p + e- + e )

+ e++ e

Epot

n p

Epot

n p

nucleus splits

- radiation

Epot

n p

+

mostly in heavy nuclei

answer to „what is radioactivity“ ?

• - radiation: split up of nucleusresulting in a lighter nucleus + 4He

• - radiation: transmutation of p (or n) into n (or p) and emission of e+ (or e-) and a (anti-)neutrino

• - radiation: transition of a p or n from a higher to a lowerenergy level with

emission of a high energy photon (keV)

nuclear fusion

in the

universe

basic astronomical facts

classification of stars: Hertzsprung-Russel diagram

luminosity

vs.

colour index

spectra of starlight

same spectra as for known elements on earth !all the same stuff .....

expansion of the universe

nebulae are other galaxiestheir light is the more shifted to longer wavelenghts the further they are away

redshift soon interpreted as expansion of the universe (Einstein‘s GTR)

sun

BAS11Z = 0.07

Big Bang nucleosynthesis

big bang at t = 0 ??? expanding universe is cooling

1ms (300 MeV) free particles

p, n, e-, e+,

s ( 1 MeV) e- p n

mn > mp neutrons decay

d = (pn) forms, but destroyed by

s (100 keV) lifetime of d increasesneutrons captured into 3T, 3He 4He

300 s ( 50 keV) nucleosynthesis finished !92% p, 7% 4He, < 1% d, 7Lino free n left

not much happens to universe of p, 4He, and e- between 5 min and 350000 y

universe needs to cool below 3000° to form H and He atoms

now GRAVITATION takes over

enormous potential gravitational energy in H and He atoms!

expansion counteracted by the formation of gas clouds of various sizescontracting gas clouds rise of T at centre „proto-star“

if mass of cloud big enough ( > 0.1 ) after several million years (My) T will rise to reionisation and eventually to neutron production !

p + p p + n + e+ +

free neutrons are back !

p + n d +

m

after 500 My: back to fusion of H to 4He

enormous stable energy release for billions of years

we understand why the sun shines

the heavier the star

the hotter in the centre

the faster it will burn

but we haven‘t found gold yet keep going ...

stellar evolution

study core: highest Tproduction of 4He increases density and T fusion speeds up

positive feed-back !

eventually all H in core burnt upfusion moves to shell, less dense „shell burning“

small star (m < 0.4 ) : H fusion will stop brown dwarf

big star: m ≈ 20 H fusion will continue mass and density of 4He and T will further increase

m

m

helium burning „ 3 process“

4He + 4He 8Be OK, but 8Be unstable with very short lifetime

need a third 4He to hit 8Be

4He + 8Be 12C „helium flash“

enormous rise of E output and T H burning in outer shell also increases

aside:

nuclei with A = 4n (multiples of 4He) dominate fusion processes

other nuclei produced as well but play little role

nuclei with odd number of p or n much less stable only 5 stable odd - odd nuclei

helium burning will produce 12C (and 16O ) in core increase of T

ignition of consecutive further burning stages

helium burning 3 4He 12C , 16O carbon burning 2 12C 24Mg 20Ne , 16O neon burning 2 20Ne 24Mgoxygen burning 2 16O 32S 28Si , 24Mgsilicium burning 2 32S 56Ni 56Co , 56Fe

all processes at the same time in consecutive shells

every new process shorter and with less E output

no more fusion processes beyond 56Fe / 56Ni !

beyond 56Fe binding energy of nucleons decreasesformation of heavier nuclei requires energy instead of releasing it

great job done ! all elements up to Fe , Ni produced

but still no gold !!?

detail: once C, N and O are presenta second H fusion process contributes: „CNO cycle“

C, N and Ojust act ascatalysts

heavy star unstable:

Fe accumulates in the core, no energy output

when mcore > 1.3 gravitational collaps e- p n

supernova explosion

m

supernova

Fe core only n collaps to incompressible nucleus

gigantic release of

nuclei falling in from outer shells stopped, partially disrupted made to bounce back as fragments release of p, n,

high energy collisions production of heavy n -rich nuclei beyond U

supernova

collapsed core will form a neutron star or a black hole

nuclei produced will settle down into full range of elements including gold !!!

ejected matter: material for new star formation

sun & solar system probably 3rd generation star

heavy elements all from previous stars

chart of nuclei

total nb. of known nuclei ≈ 3300 of which ≈ 250 (quasi-) stable

relative abundance of elements in earth crust

nAu ≈ 10-7

nFe

now we understand why gold is much rarer than iron

nuclear fusion

as

energy supply on earth ?

intriguing prospect:

practically unlimited and cheap supply of fuel: 1H, 2D, 3T

main problem:

how to attain necessary high Tto overcome electrostatic repulsion ?

brute force solution: hydrogene bomb fusion triggered by fission bomb !

first „successful“ explosions by the US (1952) and the Soviet Union (1953)

controlled fusion

60 years of technical developments: fuel (almost) always 2D and 3T

two techniques:- fusion of plasma enclosed in magnetic fields ( plasma = fully ionised atoms = bare nuclei )- inertial fusion ignition of fuel by focussed lasers or particle beams

3 critical parameters to initiate fusion:

- density- temperature of fuel (Lawson criterium )- confinement time

goal: keep fusion going for a time long enoughso that energy output > energy input

plasma fusion

enclose plasma in toroidal magnetic field „Tokamak“ „stellarator“

chamber circumference ≈ 20 m diameter ≈ 3 m

magnetic coils: no problem, field ≈ 2-5 Tesla

nuclei will spiral around magnetic field lines and around the torus

plasma current will induce poloidal field

--> instabilities

injection of 2D and 3T and acceleration to fusion temperature

fusion should keep up T n produced will escape and should heat up He gas in surrounding

large number of experimental sites all over the world

most advanced: TFTR (US) first ignition 1986JET (EU) first ignition 1991, energy O/I ≈ 0.65, 2 sec

new international project (EU, US, Russia, Japan, China, South Korea, India)

ITER International Thermonuclear Experimental Reactorin planning/construction in Cadarache (south of France)

plans: test with hydrogene plasma in 2020 ignition with 2D and 3T in 2027

goals: energy output/input ≈ 10 burning time > 400 sec

inertial fusion

main project: National Ignition Facility (Livermore, Cal., USA) driven by 192 high power lasers focussing on small target (mm)

about to reach ignition (more difficult than expected )

has also military aims

advantages of fusion reactors w.r.t. fission reactors

- fusion reactors cannot explode- unlimited supply of fuel- major radioactive material: only 3T with half-life 12.3 y

disadvantages of fusion reactors

- very expensive to construct and operate economically viable ?

summary

we wouldn‘t exist

• without the hydrogen and its gravitational potential produced during the cosmic evolution

• without all the elements produced by nucleosynthesis in the stars

• without the energy steadily supplied by the sun for billions of years

we would not exist without

nuclear fusion