[PDF] Tokamak Fusion Basics and the MHD Equations





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MHD Simulations for Fusion Applications

Lecture 1

Tokamak Fusion Basics and the MHD Equations

Stephen C. JardinPrinceton Plasma Physics Laboratory

CEMRACS '10

Marseille, France

July 19, 2010

1

Fusion Powers the Sun and Stars

Can we harness Fusion power on earth?

The Case for Fusion Energy

•Worldwide demand for energy continues to increase -Due to population increases and economic development -Most population growth and energy demand is in urban areas •Implies need for large, centralized power generation •Worldwide oil and gas production is near or past peak -Need for alternative source: coal, fission, fusion

•Increasing evidence that release of greenhouse gases is causing global climate change . . . "Global warming"

-Historical data and 100+ year detailed climate projections -This makes nuclear (fission or fusion) preferable to fossil (coal) •Fusion has some advantages over fission that could become critical: -Inherent safety (no China syndrome) -No weapons proliferation considerations (security) -Greatly reduced waste disposal problems (no Yucca Mt.)

Controlled Fusion uses isotopes of Hydrogen in

a High Temperature Ionized Gas (Plasma)

Deuterium

Tritium

Helium nuclei

-particle) ... sustains reaction NeutronDeuterium exists in nature (0.015% abundant in Hydrogen) T

Tritium has a 12 year half life: produced via

6

Li + n T +

4 He

Lithium is naturally abundantLithium

proton neutron key

Need ~ 5 atmosphere @ 10 keV

Controlled Fusion Basics

Create a mixture of D and T

(plasma), heat it to high temperature, and the D and T will fuse to produce energy. P DT = n D n T (U +U n at 10 keV, ~ T 2 P DT ~ (plasma pressure) 2

Operating

point ~ 10 keV

Note: 1 keV = 10,000,000 deg(K)

Toroidal Magnetic Confinement

Charged particles have helical orbits

in a magnetic field; they describe circular orbits perpendicular to the field and free-stream in the direction of the field.

TOKAMAK

creates toroidal magnetic fields to confine particles in the 3 rd dimension. Includes an induced toroidal plasma current to heat and confine the plasma"TOKAMAK":

Russian abbreviation

for "toroidal chamber" •500 MW fusion output •Cost: $ 5-10 B •Originally to begin operation in 2015 (now 2028 full power)

ITER is now under construction

scale

International

Thermonuclear

E xperimental Reactor: •European Union •Japan •United States •Russia •Korea •China •India •World's largest tokamak •all super-conducting coils

Tore SupraITER

ITER has a site...

Cadarache, France

June 28, 2005

Ministerial Level Meeting

Moscow, Russia

Progress in Magnetic Fusion Research

and Next Step to ITER Years

Megawatts

10 1,000 100
10 1,000 100
10100
1,000

KilowattsWattsMilliwatts

1,000 100
10

Fusion

Power

1975198519952005

Data from Tokamak

Experiments Worldwide

2015
TFTR (U.S.)JET (EU) 2025
ITER (Multilateral)

Start of

ITER

Operations

Operation with

full power test

012345678910

Power Gain

TFTR/JET ITER

050100150200250300350400450500

Power (MW) Plasma Duration

(Seconds) Power (MW)

Duration

(Seconds)

Power Gain

(Output/Input)

A Big Next Step to ITER

Plasma Parameters

Simulations are needed in 4 areas

•How to heat the plasma to thermonuclear temperatures ( ~ 100,000,000 o C) •How to reduce the background turbulence •How to eliminate device-scale instabilities •How to optimize the operation of the whole device 10 -10 10 -2 10 4 10 0 SEC.

CURRENT DIFFUSION

10 -8 10 -6 10 -4 10 2 LH-1 ci-1 A ce-1ISLAND GROWTHENERGY CONFINEMENT

SAWTOOTH CRASH

TURBULENCEELECTRON TRANSIT

(a) RF codes(b) Micro- turbulence codes(c) Extended-

MHD codes(d) Transport Codes

These 4 areas address different timescales and are normally studied using different codes Extended MHD Codessolve 3D fluid equations for device-scale stability 10 -10 10 -2 10 4 10 0 SEC.

CURRENT DIFFUSION

10 -8 10 -6 10 -4 10 2 LH-1 ci-1 A ce-1ISLAND GROWTHENERGY CONFINEMENT

SAWTOOTH CRASH

TURBULENCEELECTRON TRANSIT

•Sawtooth cycle is one example of global phenomena that need to be understood •Can cause degradation of confinement, or plasma termination if it couples with other modes •There are several codes in the

US and elsewhere that are being

used to study this and related phenomena: •NIMROD •M3D

Quicktime Movie shows Poincare plot of

magnetic field at one toroidal location •Example of a recent 3D calculation using M3D code •"Internal Kink" mode in a small tokamak (Sawtooth

Oscillations)

•Good agreement between

M3D, NIMROD, and

experimental results •500 wallclock hours and over 200,000 CPU-hours

Excellent Agreement between NIMROD and M3D

Kinetic energy vs time in lowest toroidal harmonics

M3D NIMRODM3D NIMRODFlux

Surfaces

during crash at 2 times 15

2-Fluid MHD Equations:

0 2 2

1( ) 0 continuity

0Maxwell

()momentum

Ohm's law

33
electron ener gy 22
33
22
i e ee i ie e iGV pnen nt t nMp JQt p ppt pppt JV B EB JB V VV JV JB EBB V VqV V 2 ion energy i VQ Vq

Resistive MH

2-Idea

flui D dl MHD MHD number density magnetic field current density electric field mass densityi n nM J E fluid velocity electron pressure ion pressure electron charge e i ei p p pp p eV 0 viscosity resistivity heat fluxes equipartition permeabilityQ ie q,q 16

Ideal MHD Equations:

0 ( ) 0continuit y

0Maxwell

()momentum

0Ohm's law

33energy22

i nnt t nMpt p ppt V B EB JB V VV JB EVB VV

Ideal MHD

number density magnetic field current density electric field mass densityi n nM J E fluid velocity electron pressure ion pressure e i ei p p pp pV 0 permeability 17

Ideal MHD Equations:

0 5/3 ( ) 0continuit y

0Maxwell

()momentum

0Ohm's law

33energy22

0entropyt

t p t p ppt sspst V B EB JB V VV JB EVB VV V

Ideal MHD

number density magnetic field current density electric field mass densityi n nM J E fluid velocity electron pressure ion pressure e i eiquotesdbs_dbs35.pdfusesText_40
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