Peter Paul 02/24/05

PHY313 - CEI544

The Mystery of Matter From Quarks to the Cosmos

Spring 2005 Peter Paul Office Physics D-143 www.physics.sunysb.edu

PHY313 PHY313-CEI544 Spring-05 1

What have we learned last time I

• • • We studied the nucleus. It is made up of a dense package of neutrons and protons, i.e. nucleons. The protons produce the positive charge Z that identifies the element, the N neutrons add to the mass number A = N+Z.

Nucleons interact by the strong force, which is ~ 100 time stronger than the electromag netic (EM) force. It has a range of only ~ 1 fm, about the same as the size of a nucleon.

Yukawa invented the concept of the force being mediated by the exchange of specific particles, in this case pi mesons. These exchange particles are created out of nothing, as virtual particles that live for a time given by the Heisenberg Uncertainty Relation • • • • The nuclei derive their binding from the combined effect of all the nucleons inside the nucleus.

The nucleons are packed together like water molecules in a liquid drop. Thus the volume (size) of the nucleus increases linearly with the number of nucleons, A, and the radius goes like the cube root of A: The binding energy increases as we add more nucleons, to a peak of 8.8 MeV/nucleon at the Fe (Iron) nucleus. As we add more protons the Coulomb repulsion between protons diminishes the binding of heavier nuclei. In nuclei past Pb (lead) the large Coulomb energy makes the nuclei prone to fission. After Thorium nuclei are not stable anymore.



t

  / 

E

  /

m



c

2 Peter Paul 02/24/05 PHY313-CEI544 Spring-05 2

What have we learned last time II

• Nuclei can transform themselves spontaneously by radioactive decay. Beta decay is the emission of a negative or positive electron and a neutrino. It changes a neutron into a proton or vice versa. It is mediated by the weak interaction and thus the half lives are quite long. • Radioactive decay can be used for radioactive dating, by comparing the intensity left over after a given time to that predicted by the half life of the isotope. • Positron emitters can be used for PET scanning of isotope distribution inside a human/animal body.

• To produce new isotopes or new elements one uses the fusion reaction. In this reaction two nuclei can be fused together, if they have sufficient energy to overcome their mutual Coulomb repulsion. This normally requires an accelerator.

• Neutrons, because they are not charged, can fuse with a nucleus at very low energy.

Peter Paul 02/24/05 PHY313-CEI544 Spring-05 3

The Nucleus as Energy Source: Fission

• It was already realized before WW-II that the fission process can provide a huge source of energy.

• This energy is obtained without fossil fuel combustion. It does not produce CO2 which is the source for global warming.

• The challenges were at first considered technical: Produce a controlled fission reaction, in a safe vessel that contains all radioactivity. Then find a a way to deposit and safeguard the radioactive waste that has life times of tens of thousands of years.

• Soon, however, the challenges were more a matter of public acceptance and policy. First electricity producing reactor At INEEL in the U.S. 1951 Modern nuclear reactors Peter Paul 02/24/05 PHY313-CEI544 Spring-05 4

The fission process

• The fission process for 235U:

n

 235

U

 236 92

U

*  144 56

Ba

 89 36

Kr

 3

n

• This process releases 173 MeV directly, and overall about 202 MeV, per reaction.

• It also produces 3 neutrons for each one that it used.

• More precisely, the neutron excess for different nuclei is 235 U  239 Pu  2.432 new neutrons 2.874 new neutrons • These numbers are crucial for the production of a chain reaction. • http://lectureonline.cl.msu.edu/~m mp/applist/chain/chain.htm

Peter Paul 02/24/05 PHY313-CEI544 Spring-05 5

Neutron cross sections

• Cross section area is a pictorial expression for the probability of a projectile interacting with a target nucleus.

• A Boron nucleus has a size R B ~ 2.6 fm and a nucleon has a radius R n ~ 1.2 fm Thus we expect A ~  (R B +R n ) 2 =   1240

MeVfm

 28  10 4

fm

2

mc

2

E

n

• If we take about R n ~  the cross section can be A = 2400 bn 14 x10 -26 cm 2 = 0.14 bn • A cross section area of = 10 -24 cm 2 is called a barn (bn) because it is as easy for neutrons to hit as a barn door.

• In fact Boron has a neutron capture cross section at 0.1 eV of 3,800 bn = 35,000 times what one expects: Why??

• It follows from the wave nature of the neutron that is important at low energies .

Peter Paul 02/24/05 PHY313-CEI544 Spring-05 7

Neutron reactions

• Neutron scattering as a function of neutron energy

n

 12

C



n

 12

C n

 12

C



n

'  12

C

 4 .

4

MeV

 • Neutron capture shows distinct resonances where the n is captures into excited nuclear states.

n

 235

U

 236

U



fission

Peter Paul 02/24/05 PHY313-CEI544 Spring-05 8

Multiplication factor for chain reactions

• Neutron multiplication factor

k

  

f



p

  

P

L

• If k =1 chain reaction is critical • If k< 1 chain reaction is sub critical • If k> 1 chain reaction is supercritical • • Explanation of factors in the equation:  = number of fission neutrons of any energy per initial thermal neutron absorbed in the fuel • f = fraction of thermal secondary neutrons absorbed

in the fuel

• • p = number of neutrons that escape from being thermalized  = fast fission enhancement factor • P L = neutron loss factor from volume • These values are for pure isotopes. For natural uranium the 235 U fraction is 0.72%; “weapons grade” uranium, the 235 U is enriched to at least 3% • Typical values for a 3% enriched thermal-neutron reactor:  = 1.65

f = 0.71

P = 0.87

 = 1.02 P L = 0.96

• The values produce k = 1 • For a chain reaction to build up k must be > 1.

http://lectureonline.cl.msu.edu/~mmp/applist/ch ain/chain.htm.

Peter Paul 02/24/05 PHY313-CEI544 Spring-05 9

Neutron Moderation

• In the fission process neutrons are emitted with energies between 1 and 2 Me. They must be “moderated” down to thermal energies • This is done in elastic collisions with so-called moderator material that surrounds the Uranium.

• The energy loss  = final average neutron energy/ initial neutron energy • The lighter the scattering material is the more energy the light neutron is losing in the collision:  = 0.5 for hydrogen, 0.86 for Carbon, 0.99 for Uranium • Thus light (H 2 O) and heavy (D 2 O) water are the best moderators. However, because of its propensity to absorb neutrons light water is not very good, D 2 O is in effect 100 time better, Graphite is next.

• Light and heavy water can also be used as a coolant, but not graphite. • BNL heavy water- moderated HFBR research reactor: Peter Paul 02/24/05 PHY313-CEI544 Spring-05 10

Plutonium Breeding, Xenon Poisoning & Control Material

• n-capture on 238 U can breed 239 Pu, which is an even better fission energy source than 235 U.

n

 238

U

 239

U

    239

Pu

• Thus reactors produce their own fuel while they produce energy.

• Materials that absorb neutrons very effectively act either as poisons – stopping the reactor, or as control elements-keeping the power of the chain reaction in check http://library.thinkquest.org/17940/texts/jav a/Reaction.html

• Xenon-135 was an early poison that almost stopped the Pu production at the Hanford reactors in 11943 ~ 7 hours after its start. 135 Xe has a cross section of 2.65 barns for slow neutrons.

• Good control materials are 10 B (cross section 3800 bn) and 113 Cd (20,000 bn). These materials serve in control rods that are inserted into or withdrawn from the core to absorb more or fewer neutrons.

Peter Paul 02/24/05 PHY313-CEI544 Spring-05 11

Light-water reactors

• The most widely used reactor types use water for cooling of the reactor core during the fission reaction.

• The water is either boiling or under pressure.

• In the BWR the steam heated in the reactor core directly drives the steam turbine which produces the Electricity.

• A typical reactor generates about 1000 MW of electricity.

http://www.ida.liu.se/~her/npp/demo.html

http://www.eia.doe.gov/cneaf/nuclear/page/ at_a_glance/reactors/states.html

Peter Paul 02/24/05 PHY313-CEI544 Spring-05 12

The core of the reactor is an engineering marvel

• But it is not physically complicated. It has few moving parts, mainly the control rods. • They cannot ever be allowed to get stuck in the pulled-out position or the reactor could not be controlled • The most critical parts are the cooling water pumps. If the cooling water stops the reactor will overheat and the fuel rods can melt. • Automatic safety precautions as fallbacks are incorporated into the reactor design, but these have not always been effective Peter Paul 02/24/05 PHY313-CEI544 Spring-05 13

Some facts about the fuel cycle

• Typically a reactor has about 280 fuel rods in a bundle. Typically fuel rods are changed when they become “poisoned” and replaced with new ones. The spent fuel can be re processed and Pu can be extracted.

• A modern reactor has a thermal efficiency for the production of electricity of ~32%. Thus a 1000 MWe reactor needs to produce 3100 MW of heat.

• Uranium provides “burn-up” energy of ~ 40 GWd/ton at 3.75% enrichment • 1 GWe-year requires 1.2 tons of 235 U, or 32 tons of total Uranium (3.75% enrichment) • Fuel is changes about 3 tomes/year • This requires ~ 200 tons of natural uranium. Present world demand for Uranium is ~ 60,000 tons/years, corresponding to a power production of 300 GW-years. The price of ~$260/kg or $260,000/ton.

• Spent fuel can be re-processed, with 99.8% extraction of Uranium and Pu.

• The remainder needs to be stored somewhere to cool down thermally and in terms of radiation.

Yukka Mountain Repository Peter Paul 02/24/05 PHY313-CEI544 Spring-05 14

Nuclear Reactors in the world

Peter Paul 02/24/05 PHY313-CEI544 Spring-05 15

Global warming

• production from burning fossil Energy fuels produces CO 2 which slowly accumulates in the upper atmosphere.

• CO 2 transmits the sun‘s radiation to earth but absorbs the heat radiation emitted from earth and reflects it back. This leads to global warming. • The emssion of CO 2 could be significantly reduced by use of nucler enrgy production.

• Global warming has happened before in the Earth‘s history, but leads to serious climate changes Peter Paul 02/24/05 PHY313-CEI544 Spring-05 16

The Three-Mile Island Accident

• • 3MI reactor unit 2 (~800 MW) had a serious accident on March 28, 1979 when the main cooling water pumps stopped working. The reactor fuel overheated and melted. • Although the containment vessel was not breached the publics faith in nuclear power was badly shaken. • The cause of the accident was human error, design deficiencies and component failures. • Today the 3MI-II reactor is defueled and decommis sioned.

Total cost of accident ~ $1 Billion

• Time line: March 1979: Accident happened July 1980: 43,000 Ci of Krypton vented July 1980: First human entry into reactor building Oct 1985: Defueling begun Jan 1990: Defueling completed April 1991: Evaporation of 2.23 Million g of contaminated water begins August 1993: Water removal completed Peter Paul 02/24/05 PHY313-CEI544 Spring-05 17

Some commercial power statistics

Source Fossil World (2001) 346 86% US(2002) 83.8

86% Renewable 30 7.4% 5.8

6% Nuclear 26 6.5% 8.1

8.3% Total 397 100% 98 100% Peter Paul 02/24/05 PHY313-CEI544 Spring-05 18

World Growth of Nuclear Power

US France Japan Gross generation (GWyr) 1973 World 22 Western Europe 8.4

Asia 1.4

1980 1990 2000 71 202 260 24 84 102 11 32 57 10 30 69 89 1.7

7.0

36 47 1.1

9.5

22 37 Peter Paul 02/24/05 PHY313-CEI544 Spring-05 19

Next-Generation Reactors

• The U.S. Government is beginning a program to design the next generation nuclear reactors: Generation-IV program.

• This program is studying 6 reactor concepts with the goal of having designs ready for construction by 2030. • It has dedicated the Idaho National Laboratory to this reactor development.

• The Japanese are also developing advanced concepts:

The Reduced Moderation Light water Reactor:

This reactor type leaves more energetic neutrons in the core that “burn away” heavy radioactive isotopes • In addition there is development of Thorium fueled reactors which do not produce Pu and are thus proliferation proof.

• • • • • • Gas-Cooled Fast Reactor features a fast-neutron-spectrum, helium-cooled reactor and closed fuel cycle (GFR) INEEL contact: Kevan Weaver, [email protected]

Very-High-Temperature Reactor a graphite-moderated, helium-cooled reactor with a once through uranium fuel cycle (VHTR) INEEL contact: Finis Southworth, [email protected]

Supercritical-Water-Cooled Reactor water INEEL contact: Jacopo Buongiorno, (SCWR) a high-temperature, high-pressure water-wooled reactor that operates above the thermodynamic critical point of [email protected]

Sodium-Cooled Fast Reactor conversion of fertile uranium (SFR) features a fast-spectrum, sodium-cooled reactor and closed fuel cycle for efficient management of actinides and INEEL contact: John Ryskamp, [email protected]

Lead-Cooled Fast Reactor (LFR) features a fast-soectrum lead of lead/bismuth eutectic liquid metal-cooled reactor and a closed fuel cycle for efficient conversion of fertile uranium and management of actinides INEEL contact: Kevan Weaver, [email protected]

Molten Salt Reactor (MSR) produces fission power in a circulating molten salt fuel mixture with an epithermal-spectrum reactor and a full actinide recycle fuel cycle Peter Paul 02/24/05 PHY313-CEI544 Spring-05 20

Reduced-Moderation Water Reactor (RMWR)

drier

• As a candidate of advanced light-water reactors, JAERI is now developing RMWR.

•

RMWR has a possibility of a high conversion ratio of more than 1.0.

• Gap spacing between each fuel rod is required to be only about 1 mm. • To attain the gap spacing of 1 mm, a tight-lattice core with triangular fuel rod arrangement can be needed. This requires very precise computer modeling

separator core control rod seed fuel blanket fuel

Peter Paul 02/24/05 PHY313-CEI544 Spring-05 21

Nuclear weapons

k

  

f



p

  

P L

• For a bomb the neutrons are not very well contained; in addition one needs a rapid build-up of the chain reaction, before the material flies apart. • For a nuclear bomb the uranium is highly enriched in 235 U, between 60% and 90%. • The minimum Uranium requirement is between 10 and 25 kg. For Pu bomb the minimum requirement is ~5 kg.

• If these “critical” amounts of material are in close proximity the nuclear reaction will explode.

• Two types of assembly: 1.The gun-type where an explosive charge drives a sub-critical mass into a second sub-critical mass at high speed. Uranium fuel 2.A compression type where a spherical charge compresses the nuclear fuel from a low density to a high density where it becomes critical.

Pu fuel Peter Paul 02/24/05 PHY313-CEI544 Spring-05 23

Some archive pictures

Peter Paul 02/24/05 PHY313-CEI544 Spring-05 24

Energy from Fusion in the Sun

1

H

 1

H

 2

H



e

  

e

 

e

     2

H

 1

H

 3

He

  1

H

 1

H

 2

H



e

  

e

 

e

     2

H

 1

H

 3

He

  3

He

 3

He

 4

He

 1

H

 1

H

4 1H + 2 e  4He +2 n + 6  + 26.7 MeV energy per reaction at ~ 100 Million K temperature Peter Paul 02/24/05 PHY313-CEI544 Spring-05 25

Fusion energy in the Laboratory

• The best fusion reaction is d + t   +n with an energy output of 17.6 MeV. • D and T present the lowest Coulomb barrier to fusion, and thus the lowest temperature. But it requires ~ the temperature at the core of the sun, ~100 Million degrees. At this Temperature the electrons separate from the nuclei: a Plasma http://www.jet.efda.org/ • In a thermonuclear bomb (hydrogen bomb, this temperature is produced through a fission explosion which then detonates the fusion reaction.

• For steady state operation the material needs to be held in a magnetic bottle • Both the ions and the electrons in the plasma can be held by magnetic fields. Peter Paul 02/24/05 PHY313-CEI544 Spring-05 26

Advantages and disadvantages of Fusion

• Deuterium is available from sea water, about 10x 10 12 tons. Tritium can be produced from Li through the reaction:

n

 7

Li



T

  • Sea water contains thousands of years supply of Li.

• No long-lives radioactive material is created”: Tritium half life =32 years • Fusion reactors could be continuously loaded: no poisoning of fuel.

• Fuel consumption extremely low because of huge energy production per kg of fuel.

http://fire.pppl.gov/fire_program.htm

Disadvantage: The complexity of plasma confinement and heating has held back development for 40 years!

Peter Paul 02/24/05 PHY313-CEI544 Spring-05 27

10 - 20 keV Is optimum

Peter Paul 02/24/05

~ (plasma pressure) 2

28

Confinement of plasma particles by magnetic fields

Peter Paul 02/24/05 PHY313-CEI544 Spring-05 29

Toroidal Magnetic Confinement

Charged particles have helical orbits in a magnetic field; they describe circular orbits perpendicular to the field with gyro-radius r l =v



/Ω, where Ω=qB/mc

Peter Paul 02/24/05

“TOKAMAK” (Russian abbreviation for “toroidal chamber” with magnetic fields); includes an induced toroidal plasma current to form, heat and confine the plasma

PHY313-CEI544 Spring-05 30

Product of fuel density, plasma lifetime and temperature is the “figure of merit”.

Peter Paul 02/24/05 PHY313-CEI544 Spring-05 31

As the step to ignition ITER ready to be build

500 MW of power in the plasma, plasma volume 840m 3

Toroidal Field Coil Nb 3 Sn, 18 coils Poloidal Field Coil Nb-Ti, 6 coils Central Solenoid Nb 3 Sn, 6 modules

Peter Paul 02/24/05 PHY313-CEI544 Spring-05

Blanket Module 421 modules Vacuum Vessel 9 sectors Port Plug 6 heating 3 test blankets 2 limiters rem. diagnostics Cryostat 24 m high x 28 m dia.

Divertor 54 cassettes

32

Cosmic Timeline for the Big Bang

Quarks Peter Paul 02/24/05 deuterons proton, neutrons PHY313-CEI544 Spring-05 He nuclei(  particles) 33

How are the light elements produced in stars

• Three minutes after the Big Bang the universe consisted of 75% Hydrogen, 25% 4 He less than 0.01% of D, 3 He and 7 Li.

• The sun began to burn the available H into additional 4 He, as we learned and heated itself up. • Once there was sufficient 4 He available the reaction 4 He + 4 He+ 4 He  12 C + 8 MeV became efficient. It heated the sun up still further Peter Paul 02/24/05 PHY313-CEI544 Spring-05 34

Energy from Fusion in the Sun

1

H

 1

H

 2

H



e

  

e

 

e

     2

H

 1

H

 3

He

  1

H

 1

H

 2

H



e

  

e

 

e

     2

H

 1

H

 3

He

  3

He

 3

He

 4

He

 1

H

 1

H

4 1H + 2 e  4He +2 n + 6  + 26.7 MeV energy per reaction at ~ 100 Million K temperature Peter Paul 02/24/05 PHY313-CEI544 Spring-05 35

From Helium to Carbon

• When the start has used up its hydrogen, the refraction stops and the star cools and contracts. If the star is heavy enough the contraction will produce enough heat near the core where the 4 He has accumulated to start helium burning. 4

He

 4

He

 8

Be

; 8

Be

 4

He

 12

C

• Because of gravity the heavier elements always accumulate in the core of the star.

• The star now has 4 layers: at the center accumulates the Carbon, surrounded by a He fusion layer, surrounded by a hydrogen fusion layer, surrounded by a dilute inert layer of hydrogen Peter Paul 02/24/05 PHY313-CEI544 Spring-05 36

The CNO Cycle

• Once sufficient 12 C is available it uses H nuclei to produce all the nuclei up to 16 O in a reaction cycle.

• When sufficient 16 O is available and the star has heated up muich more, the star breaks out of the CNO cycle by capture of a 4 He or a proton.

This forms all the nuclei up to 56 Fe.

• In this process energy is produced to heat the star further because the binding energy/ nucleon is still increasing.

• Hans Bethe (Cornell) and Willy Fowler (Caltech) obtained Nobel Prizes for these discoveries Peter Paul 02/24/05 PHY313-CEI544 Spring-05 37

Relative Elemental Abundances of the Solar System

1.E+02 1.E+00 1.E-02 1.E-04 1.E-06 1.E-08 1.E-10 1.E-12 0 10 20 30 40 50 Z 60 70 80 90 100

.

At least 4 processes generate heavier elements.

Peter Paul 02/24/05 PHY313-CEI544 Spring-05 38

Supernova explosion produces heavy elements

• When a star has burned all its light fuel, it cools and contracts under the gravitatio nal pressure. It then explodes. During the explosion huge numbers of neutrons are produced and captured rapidly by the exis ting elements (r-process).

• Beta decay changes neutrons into protons and fills in the elements • The new elements are blasted into space and are collected by newly formed stars. • Binary stars which are very hot can also produce the heavy elements.

Peter Paul 02/24/05 PHY313-CEI544 Spring-05 39

Z Location of the r-process in the nuclear mass table

“Magic”

Chart of the

neutron

Nuclei

numbers ...+126

“Magic” proton numbers 2,8,20,28,50,82

N=Z

The r-process works its way up the mass table on the neutron rich side . There are other processes on the proton rich side Peter Paul 02/24/05

N

PHY313-CEI544 Spring-05 40

•Heavy elements are also created in a slow neutron capture process, called the “s” process.

•The site for this process is in specific stage of stellar evolution, known as the Asymptotic Giant Branch(AGB) phase. •It occurs just before an old star expels its gaseous envelope into the surrounding interstellar space and sometime thereafter dies as a burnt-out, dim "white dwarf“ •They often produce beautiful nebulae like the

"Dumbbell Nebula"

.

•Our Sun will also end its active life this way, probably some 7 billion years from now.

Peter Paul 02/24/05 PHY313-CEI544 Spring-05 41

Fifth Homework Set, due March 3, 2005

1. Which two nuclei are used most often in nuclear fission reactors. How are these nuclei made to fission? 2. The most widely used reactor type is a lit-water reactor. What purposes does the water serve in the operation of the reactor?

3. What reaction does a fusion reactor use to produce energy and what are the principal advantages of a fusion reactor over a fission reactor that follow from using this reaction?

4. What is a nuclear chain reaction; how can it be started and can it be stopped?

5. How is the plasma in a fusion reactor kept away from the walls of the reactor vessel? What is the shape of the “bottle” that holds the plasma ?

6. What fuel does the sun burn to produce its power, and what is the “ash” left behind from the burning?

Peter Paul 02/24/05 PHY313-CEI544 Spring-05 42