# INTRODUCTION TO BURNING PLASMA PHYSICS

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1 INTRODUCTION TO BURNING PLASMA PHYSICS Gerald A. Navratil Columbia University American Physical Society - Division of Plasma Physics 2001 Annual Meeting, Long Beach, CA 1 November 2001

2 THANKS TO MANY PEOPLE WHO HELPED... BILL DORLAND BOB GROSS RICH HAWRYLUK ALI MAHDAVI DALE MEADE RIP PERKINS TOM PETRIE PETE POLITZER STEW PRAGER JIM STRACHAN JIM VAN DAM...AND OTHERS + UFA BURNING PLASMA WORKSHOP - AUSTIN UFA BURNING PLASMA WORKSHOP - SAN DIEGO FESAC BURNING PLASMA PANEL & REPORT

3 PRODUCING AND UNDERSTANDING A SUSTAINED FUSION HEATED PLASMA IS A GRAND CHALLENGE PROBLEM FOR OUR FIELD

4 DT FUSION 1 D T 3 2 He n (3.5 MeV) (14.1 MeV) σ (m 2 ) D T Energy/Fusion: ε f = 17.6 MeV D D D He Deuterium Energy (kev) 10 3 Fusion Reaction Rate, R for a Maxwellian R = σ (v ) v f D (v D ) f T (v T )d 3 v D d 3 v T where v v D v T σv (m 3 s 1 ) R = n D n T σv T (kev) /rs

5 FUSION SELF-HEATING POWER BALANCE FUSION POWER DENSITY: 1 4 p f = Rε f = n <σv>ε f for n D = n T = n 1 2 TOTAL THERMAL ENERGY IN FUSION FUEL, W = { nt i + nt e d3 x = 3nTV 2 } DEFINE ENERGY CONFINEMENT TIME, τ E W P loss ENERGY BALANCE { dw dt = 1 n <σv> ε α V + P 4 heat } W τ E α-heating power Additional heating input loss rate /rs

6 dw dt STEADY-STATE FUSION POWER BALANCE 0 P α + P heat = W τ E Define fusion energy gain, Q P fusion P heat = 5 P α P heat Define α-heating fraction, f α P α P α + P heat = Q Q+5 Scientific Breakeven Q = 1 f α = 17% Burning Plasma Regime Q = 5 f α = 50% Q = 10 f α = 60% Q = 20 f α = 80% Q = f α = 100% /rs

7 PARAMETERIZATION OF Q VERSUS ntτ E OR Pτ E Recast power balance: P α + P heat = W τ E 100 Ignition Q ~ 10 12T ntτ E = pτ E = 2 5 <σv> ε α (1 + ) Q Useful since in kev range where pτ E is minimum for given Q <σv> T 2 ntτ E (10 20 m 3 kev s) Q = 1 Q ~ 0.1 Q ~ 0.01 Q ~ and p is limited by MHD stability in Q ~ magnetically confined plasmas 10 3 Q ~ Ignition Q = pτ E > 12T 2 <σv>ε α Ion Temperature /rs

8 OUTLINE BASIC REQUIREMENTS FOR A BURNING PLASMA FRONTIER SCIENCE ISSUES: WHAT DO WE WANT TO KNOW? Q~1 RESULTS: AT THE THRESHOLD Q~5: α-effects ON TAE STABILITY Q~10: STRONG NON-LINEAR COUPLING Q 20: BURN CONTROL & IGNITION TAKING THE NEXT STEP

9 BURNING PLASMA IS A NEW REGIME: FUNDAMENTALLY DIFFERENT PHYSICS NEW ELEMENTS IN A BURNING PLASMAS: SELF-HEATED BY FUSION ALPHAS SIGNIFICANT ISOTROPIC ENERGETIC POPULATION OF 3.5 MEV ALPHAS LARGER DEVICE SCALE SIZE PLASMA IS NOW AN EXOTHERMIC MEDIUM & HIGHLY NON-LINEAR COMBUSTION SCIENCE LOCALLY HEATED GAS DYNAMICS FISSION REACTOR FUEL PHYSICS RESISTIVELY HEATED FUEL BUNDLES

10 THERE ARE TWO TYPES OF BURNING PLASMA ISSUES... GETTING THERE & STAYING THERE: + DENSITY, TEMPERATURE, AND τ E REQUIRED FOR Q 5 + MHD STABILITY AT REQUIRED PRESSURE FOR Q 5 + PLASMA EQUILIBRIUM SUSTAINMENT (τ > τ SKIN ) + POWER, FUELING, & REACTION PRODUCT CONTROL NEW SCIENCE PHENOMENA TO BE EXPLORED + Q 5: ALPHA EFFECTS ON STABILITY & TURBULENCE + Q 10: STRONG, NON-LINEAR COUPLING BETWEEN ALPHAS, PRESSURE DRIVEN CURRENT, TURBULENT TRANSPORT, MHD STABILITY, & BOUNDARY- PLASMA + Q 20: STABILITY, CONTROL, AND PROPAGATION OF THE FUSION BURN AND FUSION IGNITION TRANSIENT PHENOMENA

11 IMPORTANT PHYSICAL PROPERTIES OF α-heating FOR Q ~ 10: ntτe ~ 2 x m -3 kev s for T ~ 10 kev + WHEN NON-IDEAL EFFECTS (PROFILES, HE ACCUMULATION, IMPURITIES SOMEWHAT LARGER VALUE ~ 3 X m -3 kev s FOR TOKAMAK TYPICAL PARAMETERS AT Q ~ 10 n ~ 2 x m -3 T ~ 10 kev τ E ~ 1.5 s BASIC PARAMETERS OF DT PLASMA AND α v Ti ~ 6 x 10 5 m/s v α ~ 1.3 x 10 7 m/s v Te ~ 6 x 10 7 m/s Note at B ~ 5 T: v Alfvén ~ 5 x 10 6 m/s < v α CAN IMMEDIATELY DEDUCE: 1) α-particles MAY HAVE STRONG RESONANT INTERACTION WITH ALFVEN WAVES. 2) T i ~ T e since v α >> v Ti AND m α >> m e THE α-particles SLOW PREDOMINANTLY ON ELECTRONS.

12 HOW CLOSE ARE WE TO BURNING PLASMA REGIME? Tokamak experiments have approached Q ~ 1 regime.

13 Q 1 Results from TFTR and JET At the Burning Plasma Threshold

14 DT EXPERIMENTS ON TFTR AND JET Peak Transient Q α Confinement α Slowing Down Classical Classical α Heating Observed Yes, but weak Yes α Driven Alfven Waves in Highest P α Plasmas TFTR 0.27 Classical No JET 0.61 Classical No T i 36 kev 28 kev T e 13 kev 14 kev n m m 3 ntτ m 3 kevs m 3 kevs f α 5% 12% [~2MW] [~3 MW] /rs

15 FUSION ALPHAS ARE CONFINED AND SLOW DOWN CLASSICALLY IN TFTR Intensity (10 10 ph/s-cm 2 -ster) E α = MeV Minor Radius (r/a) Experiment Classical Slowing Down Model: D α =0 (w/error band) D =0.03 m 2 /s JET reports same conclusion using detailed modeling of α-heating power balance. α

16 JET DT EXPERIMENTS SHOW α-heating OF CENTRAL ELECTRONS D/T ratio varied & maximum T e ~ 3 kev at 60% T

17 NO α-driven ALFVENIC INSTABILITIES SEEN IN TFTR AND JET IN HIGHEST FUSION POWER DT PLASMAS AE stable due to strong damping by beam and plasma ions in NBI heated hot ion mode plasmas. AE modes were observed in equilibria with low shear and higher central q just after NBI turned off.

18 Q ~ 5: α-effects ON TAE STABILITY

19 ALPHA PARTICLE EFFECTS: KEY DIMENSIONSLESS PARAMETRS l Three dimensionless parameters will characterize the physics of alpha-particle-driven instabilities: Alfven Mach Number: V α /V A (0) Number of Alpha Lamor Radii (inverse): ρ α /a Maximum Alpha Pressure Gradient (scaled): Max R β α Range of Interest (e.g. ARIES-RS/AT) ITER-FEAT (reference) FIRE (reference) JET V α /V A (0) ρ α /a ~0.1 Max R β α * /rs

20 GEOMETRIC EFFECTS ON ALFVEN WAVES Continuous spectrum, shear Alfvén resonance

21 GEOMETRIC EFFECTS ON ALFVEN WAVES Add 2D toroidal effects: Periodic boundary conditions for toroidal mode number, n, and poloidal mode number, m m and m+1 are coupled and a gap is opened in the otherwise continuous spectrum

22 GEOMETRIC EFFECTS ON ALFVEN WAVES Add elliptical cross-section effects: m and m+2 are now coupled and an elliptical gap is opened in the continuous spectrum Add triangularity cross-section effects: m and m+3 are now coupled and an triangularity gap is opened in the continuous spectrum

23 GEOMETRIC EFFECTS ON ALFVEN WAVES Discrete Modes Appear in Gaps in the Continuum: Alfvén wave continuum is strongly damped. TAE gap-modes are less damped: free energy from p α tapped by wave/particle resonance drive from α-particles may destabilize these modes.

24 BASIC ALFVEN EIGENMODE PHYSICS EXTENDS TO RANGE OF TOROIDAL CONFIGURATIONS Tokamak: Stellarator: Spherical Torus: Details of spectra differ but underlying physics and modeling tools are common.

25 New Alpha Effects Expected on Scale of Burning Plasma Present experiments show alpha transport due to only a few global modes. Smaller value of ρα/<a> in a Burning Plasma may lead to a sea of resonantly overlapping unstable modes & possible large alpha transport. Reliable simulations not possible...needs experimental information in new regime. This and other alpha physics will be discussed in more detail in next talk by Bill Heidbrink...

26 Q ~ 10: Strong Non-Linear Coupling

27 BURNING PLASMA SYSTEM IS HIGHLY NON-LINEAR... BASIC COUPLING OF FUSION ALPHA HEATING:

28 BURNING PLASMA SYSTEM IS HIGHLY NON-LINEAR... ADD ALPHA DRIVEN TAE MODES:

29 BURNING PLASMA SYSTEM IS HIGHLY NON-LINEAR... ADD COMPLEX PHYSICS OF ALPHA DRIVEN TAE MODES:

30 MAJOR DISCOVERY OF THE 1990 s: ION TURBULENCE CAN BE ELIMINATED Color contour map of fluctuation Total ion thermal diffusivity at time intensity as function of time from FIR scattering data Higher frequencies correspond to core, low to edge of peak performance H = 4.5 W = 4.2 MJ β = 6.7% βn = 4.0 NCS H mode edge intensity map } core } edge χtot = Q /n T 10.0 i start of L H transition high power NBI n=2 mode begins peak neutron rate i i i Neoclassical Experiment 1.00 i 0 χtot (m2/s) Frequency (khz) Neutron Rate (x1016/s) jy Time (ms) RADIUS (NORM.) 1

31 With Flow Without Flow SHEARED FLOW CAUSES TRANSPORT SUPPRESSION Gyrokinetic Theory Simulations show turbulent eddies disrupted by strongly sheared plasma flow Growth, shearing rates (10 5 s 1 ) Fluctuation level δn/n (%) ERS transition Experiment Turbulent fluctuations are suppressed when shearing rate exceeds growth rate of most unstable mode Shearing rate Growth rate Time (s) 2.75 y

32 Combination of Turbulence Suppression & Bootstrap Current Leads to Steady-State Advanced Tokamak Data from JT-60U shows sustained transport barrier and 100% non-inductive current drive

33 PLASMA BOUNDARY PHYSICS: HEAT REMOVAL & CONFINEMENT EDGE PEDESTAL STRONGLY COUPLED TO CONFINEMENT: INTERNAL T LIMITED BY MICROTURBULENCE SO EDGE T CONTROLS CENTRAL FUSION REACTIVITY: P FUSION ~ [T EDGE ] 7 HEAT REMOVAL SOLUTIONS TREND TO HIGH EDGE DENSITY BUT BOOTSTRAP CURRENT SUSTAINED STEADY-STATE PLASMAS TREND TOWARDS LOWER EDGE DENSITY: COMPATABILITY AN OPEN ISSUE IN BURNING PLASMA REGIME ENERGETIC IONS MODIFY : COUPLING TO α-particles.

34 Pedestal Temperature Requirements for Q=10 Device Flat new Peaked ne Peaked ne w/ reversed q * IGNITOR FIRE v ITER-FEAT l kev kev kev w flat density cases have monotonic safety factor profile * n / n = 1.5 with n held fixed from flat density case eo ped ped v 10 MW auxiliary heating 11.4 MW auxiliary heating l 50 MW auxiliary heating DIII D NATIONAL FUSION FACILITY SAN DIEGO JEK - BP2001

35 ADVANCED TOKAMAK NONLINEAR TRANSPORT COUPLINGS Transformer source of poloidal flux Auxiliary Current Drive Auxiliary Heating Auxiliary Angular Momentum External V loop j cd Internal Thermonuclear Heating j Oh Bootstrap Current dp/dr p, T, n Profiles: p,t,n,v φ P tot p, T, n, v φ Fast, Blue heat and v φ transport cycle j bs p, T, n, v φ Anomalous & Neoclassical heat, particle and v φ diffusion Neoclassical poloidal flux diffusion Β θ σ Conductivity profile T χ s Turbulent and Neoclassical transport coefficients χ Poloidal field dependence Velocity shear stabilization Temperature profiles couple magnetic and heat diffusion loops Slow, red magnetic flux diffusion loop

36 Q > 20: Burn Control & Ignition Transient Phenomena

37 TRANSIENT BURN PHENOMENA WHEN Q ~ > 20 Time dependent energy balance: d [ 3 nt ] = 1 n ε α V <σv> + P heat 3 nt dt 4 τ E (n,t) At fixed n and high Q system can be thermally unstable Solve for P heat in steady-state: P heat = 3 nt τ E (n,t) 1 4 n ε α V <σv> Ignition n n T T (kev) /rs

38 TRANSIENT BURN PHENOMENA WHEN Q ~ > 20 Time dependent energy balance: d [ 3 nt ] = 1 n ε α V <σv> + P heat 3 nt dt 4 τ E (n,t) At fixed n and high Q system can be thermally unstable Solve for P heat in steady-state: P heat = 3 nt τ E (n,t) 1 4 n ε α V <σv> n Unstable Path Ignition n T T (kev) /rs

39 TRANSIENT BURN PHENOMENA WHEN Q ~ > 20 Time dependent energy balance: d [ 3 nt ] = 1 n ε α V <σv> + P heat 3 nt dt 4 τ E (n,t) At fixed n and high Q system can be thermally unstable Solve for P heat in steady-state: P heat = 3 nt τ E (n,t) 1 4 n ε α V <σv> Ignition n Stable Path n T T (kev) /rs

40 MORE REALISTIC POWER BALANCE ITER POPCON Power Balance Analysis Additional limits on density, pressure, & power thresholds constrain operating space.

41 FUSION BURN PROPAGATION AT HIGH Q l Deflagration sub-sonic Mediated by diffusive thermal conductivity, χ δ T V b Diffusive Time Scale τ d ~ δ 2 Fusion Burn Time Scale χ τ burn ~ x W P f In steady-state τ d ~ τ burn δ ~ χw P f V b ~ δ ~ τ burn χp f W /rs

42 FUSION BURN PROPAGATION AT HIGH Q EXAMPLE PARAMETERS n ~ 4 X m -3 T ~ 20 kev Pα ~ 10 MW/m 3 W = 3nT ~ 3.8 MJ/m 3 δ ~ 0.2 m V b ~ 0.5 m/s χ ~ 0.1 m 2 /s

43 Comments on Next Steps for Study of Burning Plasmas

44 Major Advances & Discoveries of 90 s Lay Foundation for Next Step Burning Plasma Experiments Burning Plasma Experiment MHD Transport & Turbulence Wave/Particle Interactions Plasma Wall Interactions q-profile control and measurement steady-state, bootstrap equilibria active mode control of kink & tearing shear-flow turbulence suppression gyro-kinetic theory based models extensive data-base models on transport using dimensionless scaling alpha heating in DT found to be classical for Q 1 standard model of Alfvén Eigenmodes LHCD & ECCD used for near SS & mode control detached divertor demonstrated large scale models developed high heat-flux metallic technology developed

45 Modest Confinement Extrapolation Needed for BP Dimensionless Parameters ω c τ ρ* = ρ/a ν* = ν c /ν b β x X FIRE ITER-EDA ITER-FEAT Bτ Eth Similarity Parameter B R 5/4 Kadomtsev, 1975 Bτ Eth ~ ρ* 2.88 β 0.69 ν* 0.08

46 CONCLUDING COMMENTS & DISCUSSION BURNING PLASMA STUDIES OPEN A NEW REGIME OF PLASMA PHYSICS OF AN EXOTHERMIC MEDIUM: IS THE GRAND CHALLENGE PROBLEM IN OUR FIELD. PHYSICS BASIS FOR BURNING PLASMA STEP WAS NEARLY IN HAND IN 1986 WITH PROPOSALS FOR CIT & LATER BPX : IF BUILT WE NOW KNOW IT WOULD HAVE REACHED Q > 5. DRAMATIC PROGRESS IN 1990 S HAS ESTABLISHED A SOUND BASIS FOR EXPLORATION OF THE BURNING PLASMA REGIME. WE MUST WORK TOGETHER NOW TO TAKE THIS IMPORTANT BURNING PLASMA STEP. Columbia University

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