Discovery Research in Magnetic Fusion Energy or “How we learn about magnetic containment and the potential to reduce the cost of fusion energy with alternate configurations” Mike Mauel Columbia University http://www.columbia.edu/~mem4/ ! National Undergraduate Fusion Fellowship Program 13 June 2014 ! The slides for this talk are online at: http://www.apam.columbia.edu/mauel/mauel_pubs/NUF2014-DiscoveryMagFusion.pdf Outline • Columbia University’s plasma physics experiments

• Plasma containment depends upon the shape of the magnetic field

• What can we learn by changing magnetic topology? Examples…

• Stellarator: optimizing the helical plasma torus

• Spheromak: Magnetic self-organization

➡ Levitated dipole: “simplest” axisymmetric magnetic confinement

• Fusion energy needs discoveries to overcome challenges to economic viability

• Over 200 tokamaks and soon there will be ITER… We know a lot about the challenging economics of tokamak-based fusion energy

• Discoveries are needed from creative new scientific investigations (2004)

Columbia University Collaborator Dr. Otto Octavius Stabilize Fusion in NYC… Magnetized Plasma Physics Research at Columbia University

A %XTERNALTOVESSELFERRITICWALLOPTION

• CNT Stellarator FERRITICMATERIAL

B )N VESSELFERRITICWALLOPTION

• HBT-EP Tokamak FERRITICMATERIAL

• CTX/LDX Dipole Magnetized Plasma Physics Research at Columbia University

• CNT Stellarator

• HBT-EP Tokamak

• CTX/LDX Dipole How Do Magnetic Fields Confine Ionized Matter?

Equations of magnetic confinement… Plasma Pressure (No monopoles) B =0 Plasma ⌅ · (No charge accumulation) J =0 Current ⌅ · (No unbalanced forces) 0 = P + J B ⌅ ⇤ (Magnetostatics) B = µ J ⌅⇤ 0

Magnetic Torus How Do Magnetic Fields Confine Ionized Matter?

Equations of magnetic confinement… Plasma Pressure (No monopoles) B =0 Plasma ⌅ · (No charge accumulation) J =0 Current ⌅ · (No unbalanced forces) 0 = P + J B ⌅ ⇤ (Magnetostatics) B = µ J ⌅⇤ 0 Surfaces of constant Magnetic Torus plasma pressure form nested tori J B = P ⇥ ⇤ B P =0 · ⇤ J P =0 not so easy without · ⇤ symmetry (chaotic fields) Four Plasma Tori

• Axi-symmetric toroid with external poloidal currents (fails)

• Axi-symmetric toroid with internal toroidal current (“levitated dipole” inside the plasma)

• Axi-symmetric toroid with (mostly) external poloidal currents and (mostly) plasma toroidal current (“tokamak”)

• Non-symmetric plasma torus with external helical coils (“stellarator”) How FAILSto make TO CONFINE a magnetic PARTICLES torus?

Coil Current

Toroidal Field from Poloidal Currents How to make a magnetic torus?

Coil Current

Poloidal Field from Toroidal Currents How to make a magnetic torus?

Plasma Current

Combined Toroidal and Poloidal Field (Tokamak) How to make a magnetic torus? 3.3 m

1.7 m

1.8 m

HBT-EP Columbia University

NSTX-U DIII-D PPPL General Atomics Combined Toroidal and Poloidal Field (Tokamak) More than 200 Tokamaks (We know how tokamaks work relatively well.)

ITER Magnetic Fusion Optimization Depends on Shape Fundamentally, the behavior of magnetically-confined plasma depends upon the shape of the magnetic flux tube…

Interchange Instability Bending Field ➠ Effective g How to make a magnetic torus? High q ← Increasing Toroidal Field ← Low q

Fundamentally, the behavior of magnetically-confined plasma depends upon the shape of the magnetic flux tube…

Combined Toroidal and Poloidal Field (Tokamak) How to make a magnetic torus?

Helical Coils (Wound in Place)

+Toroidal Currents

Non-symmetric plasma torus with (mostly) external helical currents (Stellarator) How to make a magnetic torus? Quasi-Isodynamic Torsatron (no parallel currents)

Heliac

Quasi-Symmetry (Like tokamak along helical path)

Non-symmetric plasma torus with (mostly) external helical currents (Stellarator) Why study different magnetic tori?

• Fundamental study • Confinement science, heating, sustainment, heat flux to boundaries, fluctuations, instabilities, complex behaviors of high-temperature matter, magnetized “bright matter” throughout the universe, …

• Fusion energy • Magnetic torus has to “work” and make fusion • Achieve fusion’s promise of safety and environmental attractiveness • Have economically viable applications (like high payload space power and propulsion, non-carbon electrical power on Earth, …) Toroidal Magnetic Configurations Self-Organized

FRC

RFP High Toroidal Field! Low Toroidal Field! High q Low q

ST

Tokamak Dipole

Externally Controlled

NRC BP (Mauel) 19 NRC BP (Mauel) 20 Outline

• Plasma containment depends upon the shape of the magnetic field

• What can we learn by changing magnetic topology? Examples…

• Stellarator: optimizing the helical plasma torus

➡ Levitated dipole: “simplest” axisymmetric magnetic confinement

• Spheromak: Magnetic self-organization

• Fusion energy needs discoveries to overcome challenges to economic viability

• Over 200 tokamaks and soon there will be ITER: what we know about the economics of tokamak-based fusion energy

• Discoveries are needed from creative new scientific investigations

• Columbia University’s plasma physics experiments Levitated Dipole Experiment

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7 Launcher/Catcher MIT Plasma Science & Fusion Center 09/24/2006 11:11 PM

Administration Computers & Networks Calendar Safety Search PSFC Search

8 Channel Plasma Science & Fusion Center

Laser Detection Massachusetts Institue of Technology and RT Controller Electron

Cyclotron Waves

About PSFC Research People Education News & Events Library General Info

The Plasma Science & Fusion Center (PSFC) is recognized as one of the leading university research laboratories in the physics and engineering aspects of magnetic

confinement fusion. 2 m

77 Massachusetts Avenue, NW16, Cambridge, MA 02139 phone: 617-253-8100, [email protected]

http://www.psfc.mit.edu/ Page 1 of 1 Lifting, Launching, Levitation, Experiments, Catching

J. Belcher First Levitated Dipole Plasma Experiment Discover a New Regime by Linking Space and Laboratory Science

• Leveraging space physics to discover a Fast Particles in Space and Lab

new regime: axisymmetric, steady-state, Cassini (Jan 2001) Hot Electron Radio Emission compressibility (ω* ~ ωd), β ~ 1, no field- aligned currents, shear-free, bounce-averaged gyrokinetics, wave-particle dynamics, …

• Magnetospheric configuration but not a “miniature magnetosphere” (high β stability but without polar losses and Hot Electron LDX (Jul 2005) X-Ray Emission field-aligned currents)

• Toroidal magnetic confinement, but not a “miniature fusion reactor” (controlled tests of transport, stability, and self- organization) Our Space Environment is Complex and Highly Variable With Concurrent Plasma Processes and Important Questions to Answer

Van Allen Probes (A&B) Launched August 2012 Discovered New 3rd Radiation Belt (2 MeV e-) then annihilated by passage of interplanetary shock ScienceExpress, Baker, et al., 28 Feb 2013 INNER MAGNETOSPHERIC MODELING WITH THE RICE CONVECTION MODEL

FRANK TOFFOLETTO, STANISLAV SAZYKIN, ROBERT SPIRO and RICHARD WOLF Department of Physics and Astronomy, Rice University, Houston, TX 77005, U.S.A.

Abstract. The Rice Convection Model (RCM) is an established physical model of the inner and middle magnetosphere that includes coupling to the ionosphere. It uses a many-fluid formalism to describe adiabatically drifting isotropic particle distributions in a self-consistently computed electric field and specified magnetic field. We review a long-standing effort at Rice University in magneto- spheric modelingINNER with the MAGNETOSPHERIC Rice Convection Model. MODELINGAfter briefly describing WITH theTHE basic RICE assumptions Electrons andINNER equations MAGNETOSPHERIC that make up the core ofCONVECTION the RCM, we MODELING present MODEL a sampling of WITH recent results THE using the RICE Ions model. We conclude with a briefCONVECTION description of ongoing and MODEL future improvements to the RCM. Key words: magnetosphere-inner,FRANK TOFFOLETTO, numerical STANISLAV modeling, plasma SAZYKIN, convection, ROBERT ring SPIRO current and RICHARD WOLF FRANK TOFFOLETTO,Department of Physics and STANISLAV Astronomy, Rice University, SAZYKIN, Houston, TXROBERT 77005, U.S.A. SPIRO and 180 Semi-collisional FRANKPlasmasphere1.RICHARD Introduction TOFFOLETTO WOLF ET and AL. Ring Current Department of Physics and Astronomy, Rice University, Houston, TX 77005, U.S.A. Earth’s inner magnetosphere is home toTABLE an interesting I variety of particle popula- tions andAbstract. plasmaComparisonThe processes. Rice Convection of equations While Model radiation-belt of (RCM) ideal is MHD an established particles with those physical (> 1MeVenergy)have used model in of the the RCM inner and been elegantlymiddle magnetosphere described that by includes the adiabatic coupling to theorythe ionosphere. developed It uses a in many-fluid the earliest formalism days to describe adiabatically drifting isotropic particle distributions in a self-consistently computed electric Electrons Ions of theIdealfield space MHD and age specified e.g., magnetic (Northrop, field. We 1963), review aRCM this long-standing picture effort can at be Rice disrupted University inby magneto- severe Electrons For eachIons species and invariant energy λ, η is solar-windspheric disturbances modeling with the (Li Riceet Convection al.,1993).Theringcurrent,consistingmainlyof Model. After briefly describing the basic assumptions ∂ρ ∂ conserved along a drift path. ions and∂tand electrons equations(ρv) that in make0 the up 10–200 the core of KeV the RCM, energy( ∂t we presentv range,k(λk a, samplingx,t) carries of) aη recentk large resultsS( fractionηk using) L( the ofηk) Abstract. The∂model.+ Rice∇ We· Convection conclude= with a Modelbrief description (RCM) of ongoing is+ an⃗ and established future⃗ improvements·∇ physical= to the model RCM.− of the inner and the total( particlev )( energyρv) ofj theB magnetosphereP jk B and enoughPSpecifick current Entropy to substantially! middle magnetosphere∂t +⃗·∇ that⃗ includes= ⃗ × ⃗ coupling−∇ to⃗ the× ⃗ ionosphere.=∇ It uses a many-fluidγ formalism2 to affect the∂Key overall words: magnetosphere-inner, magnetic5/3 configuration. numerical modeling, Coexisting2 plasma in convection, the same5 ring/3 region current of spacepV = λ η ( ∂t v )(Pρ− ) 0 P 3 k ηk λk V − ,λk constant ∑ s s describe adiabatically+⃗·∇ drifting isotropic= particle distributions= | in a| self-consistently= computed3 electrics as the radiationB 0P belt and ring current is theart plasmasphere,ofthemagnetic consistingfieldmode mainlyl. of field andparticles specified∇· with⃗ = magnetic energies field.< 1eV.Whiletheplasmaspheredoesnotdirectlyaffectthe We review a long-standing! effort at Rice University in magneto- B µ j Included in magnetic field, but j j . sphericmagnetospheric modeling∇× ⃗ with= themagnetic0 ⃗ Rice Convection field configuration, Model. it After still contains briefly describing most of the⃗ the̸ mass= basick of⃗k assumptions ∂B 1. Introduction and equationsthe magnetosphere. thatE make up⃗ The the plasmasphere core of the RCM, exhibitsIncluded we a present wide implicitly range a sampling in of mapping. interesting of recent plasma results using the ∇× ⃗ =−∂t ! model. Wephenomena concludeEarth’s which with inner affect a magnetosphere brief wave description propagation, is home of toongoing anparticle interesting and loss, future variety and heating improvements of particle processes popula-W( toλk, in thex,t) RCM. E v B 0 E B 0andE vk B ∇ q ⃗ the ring⃗tions+ current⃗× and⃗ plasma and= radiation processes. belt While populations. radiation-belt⃗ · ⃗ = particles⃗⊥ (+> 1MeVenergy)have⃗ × ⃗ = k Key words:Becausemagnetosphere-inner,been elegantly many space-based described numerical by assets the adiabatic are modeling, located theory in plasma the developed inner convection, magnetosphere in the earliest ring current days and For each species and invariant energy λ, η is the underlyingof theFor space ionosphere, each age e.g., species (Northrop,understanding and 1963), invariant the this physical picture energy processes can be disruptedλ, thatη is control by severe this conserved along a drift path. regionsolar-wind of spaceconserved has disturbances important along (Li spaceet a al. drift weather,1993).Theringcurrent,consistingmainlyof path. implications. For example, the per- formanceions of and geosynchronous electrons in the communications 10–200 KeV energy spacecraft range, carries can be a impaired large fraction by the of Specific Entropy! 2 guaranteethe that totalSpecific the particle current energyEntropy density of the! magnetosphere carried by each and enough species currentk,crossedwiththemag- to substantially γ effects of surface charging and the resultant2 arcing in solar panels. MeV outer- pV = λs ηs netic field,affect balances the overall the magnetic gradient configuration.pV ofγ the partial Coexisting pressure in the same for region species of spacek,underthe 3 ∑ belt ‘killer electrons’ constitute another1. Introduction important= ∑ λ space-weathers ηs hazard; they are s assumptionas the that radiation the inertial belt and termsring current in the is3 the momentums plasmasphere, equation consisting mainly are negligible. of In the RCM,particles the adiabatic-compression with energies < 1eV.Whiletheplasmaspheredoesnotdirectlyaffectthe condition takes the form of assuming that Earth’s innerSpacemagnetospheric magnetosphere Science Reviews magnetic107: is175–196, field home configuration, 2003. to an interesting it still contains variety most of the of mass particle of popula- the energy©2003 invariantKluwer Academicλ is Publishers. conserved. Printed Magnetic in the Netherlands. field models used as input to the tions and plasmathe magnetosphere. processes.k The While plasmasphere radiation-belt exhibits a wide particles range of interesting (> 1MeVenergy)have plasma classical RCMphenomena always which assume affect wave propagation,B 0. While particle those loss, and input heating models processes also in generally been elegantly described by the adiabatic⃗ theory developed in the earliest days satisfy a conditionthe ring current andB radiationµ∇ beltj·,thecurrentusedinthemagneticfieldmodelis, populations.= of the space ageBecause e.g., many∇× (Northrop, space-based⃗ = 0 ⃗ assets 1963), are located this picture in the inner can magnetosphere be disrupted and by severe in general,the not underlying constrained ionosphere, to understanding be equal to the the physical sum processes of the RCM-computed that control this partial solar-windcurrents j disturbancesregion;however,someRCMrunsarenowbeingperformedusingamagnetic of space has (Li importantet al. space,1993).Theringcurrent,consistingmainlyof weather implications. For example, the per- ⃗k ionsfield and that electronsformance is consistent of in geosynchronous the with 10–200 RCM-computed communications KeV energy spacecraft currents range, can (Section carries be impaired a 5). largeby As the discussed fraction of effects of surface charging and the resultant arcing in solar panels. MeV outer- thepreviously total particlebelt Faradays ‘killer energy electrons’ law of theconstitute is included magnetosphere another in important the RCM and space-weather enough implicitly, hazard; current through they to are substantially the time- affectdependent the overall mapping magnetic between configuration. ionosphere and Coexisting magnetosphere. in the Like same MHD, region the of RCM space asgenerally the radiation assumesSpace belt Science that and Reviews there ring107: current is175–196, no electric 2003. is the field plasmasphere, component consisting along the magnetic mainly of ©2003Kluwer Academic Publishers. Printed in the Netherlands. particlesfield; however, with energies the RCM< 1eV.Whiletheplasmaspheredoesnotdirectlyaffectthe drift equation includes the effect of gradient-curvature magnetosphericdrifts, which is magnetic equivalent field to writing configuration, a separate it Ohm’s still contains law for most each species of the massk and of theincluding magnetosphere. an extra The gradient/curvature plasmasphere term. exhibits a wide range of interesting plasma phenomena which affect wave propagation, particle loss, and heating processes in the ring current and radiation belt populations. Because many space-based3. assets RCM are Algorithms located in the inner magnetosphere and the underlying ionosphere, understanding the physical processes that control this Figure 1 outlines the essential logical structure of the RCM. This chart elaborates regionthe basic of space scheme has first important proposed space by (Vasyliunas, weather implications. 1970). The For differences example, between the per- formancethe scheme of geosynchronous shown in Figure communications 1 and that given spacecraft by Vasyliunas can be are impaired the additional by the effectsboxes of representing surface charging various and model the inputs resultant and arcing outputs in as solar well as panels. modifications MeV outer- to beltinclude ‘killer such electrons’ effects constitute as self-consistently another important computed space-weather ionospheric conductance. hazard; they The are core of the calculation, in the center of the figure, displays the basic algorithmic timeSpace loop. Science The Reviews RCM steps107: in175–196, time (typically 2003. with steps of 1–5 sec.), iteratively solving©2003 EquationsKluwer Academic (4) and Publishers. (12), with time-dependent Printed in the Netherlands. inputs. Equation (4) is used to advance the particles, using the velocity computed from Equation (1). Equation (1) Self-Organized Mixing: Dye Stirred in Glass CHAPTER 5. MAGNETIC RECONSTRUCTIONS: RESULTS 88 New Regime: High β, Turbulent Self-Organized, Steady-State Supported shot 100805045 Levitated shot 100805046 Self-Organized, Steady-State Profiles atS100805046 High β • 20 kW injected electron cyclotron waves

• Density proportional10.5 GHz on to injected power10.5 GHz off 10.5 GHz on 10.5 GHz off 6.4 GHz off 6.4 GHz off 6.4 GHz on 6.4 GHz on • Plasma2.45 GHz energy on proportional2.45 GHz to offpower 2.45 GHz on 2.45 GHz off • Peak plasma density 1012 cm-3

• Plasma energy 250 J (3 kA ring current)

• Peak β ~ 40% (100% achieved in RT-1)

• Classical fast particles〈Eh〉~ 54 keV

• Peak〈Te〉> 0.5 keV (thermal)

Sustained, dynamic, steady state … • Plasma density and electron pressure naturally approach “canonical” profile shape determined magnetic flux-tube volume, δV. • Density evolves at rates described by bounce-averaged gyrokinetic theory. Time [sec] Time [sec]

Figure 5.1: Overview of supported shot 100805045 and levitated shot 100805046. The top row shows that the heating power profile was the same in both shots. The second row shows that the vessel pressure was similar on both shots. The third row shows that during levitation the change in the magnetic flux measured by a flux loop at the outer mid-plane (diameter 5 m) is nearly a factor of two greater than during supported operation. The last row shows the phase measurement of the 4 chord interferometer: black (77 cm tangency radius), red (86 cm), green (96 cm), and blue (125 cm). The large phase change on the inner chords during levitation show that the electron density is much higher and centrally peaked during levitated operation. The light red and light blue vertical lines indicate the times used in the reconstructions described in the next sections. The vertical black lines mark times when the input power changes. Quantitative Verification of Inward Turbulent Pinch @(¯nV ) @ @(¯nV ) = S + D @t h i @ @ Line Density Shows Strong Pinch (a) Side View With levitated dipole, inward turbulent Onlytransportwith a setsLe vprofileitate devolutionDipole

Levitated

Upper Hybrid Turbulent pinch Resonances from measured Cyclotron fluctuations Resonances

Supported 25 msec ECRH 3 msec Catcher Catcher CatcherCatcher Open Raised Field-Lines 4 Channel Raised LoweredLowered Interferometer (b) Top View InterArrayferometer

Alex Boxer, et al., “Turbulent inward pinch of plasma confined by a levitated dipole magnet," Nature Phys 6, 207 (2010).

Closed Field-Lines Heating or gas modulation demonstrates (Robust) inward pinch & Natural “canonical” profile

• Density increases with power (T ~ constant). Density profile shape is unchanged near (nδV) ~ constant. • Gas source moves radially outward. Inward pinch required to increase central density.

15 15 1.0 1.0 S100528019 S100528019 12 S100528019 Interferometer (Rad) 12 S100528019 Interferometer (Rad) Density (×10 Particles/cc) 5.100 sec Density (×10 Particles/cc) 5.100 sec 5.150 sec 5.150 sec 10 10 0.8 0.8

5 5 25 kW ECRH nL2 25 kW ECRH nL2 0.6 nL3 0.6 nL3 0 0 Line Density Ratio (nL2/nL3) Line Density Ratio (nL2/nL3) 1.8 1.8 0.4 15 kW ECRH (nδV) ~ constant 0.4 15 kW ECRH 1.6 1.6

1.4 1.4 0.2 0.2 1.2 1.2

1.0 1.0 0.0 ECRH Power (kW) 0.0 ECRH Power (kW) 25 25 〈S〉 〈S〉 30 Flux-Tube Integrated 20 30 Flux-Tube Integrated 20 Particle Source from Particle Source from 15 15 20 Light Emission (A.U.) 20 Light Emission (A.U.) 10 High Power 10 High Power 10 10 5 5 Low Power Low Power 0 0 0 0 0.6 0.8 1.0 1.2 1.4 1.6 1.8 5.00 5.05 5.10 5.15 5.20 0.6 0.8 1.0 1.2 1.4 1.6 1.8 5.00 5.05 5.10 5.15 5.20 Radius (m) time (s) Radius (m) time (s) Turbulent Pinch is a Fundamental Process found in Toroidal Magnetic Systems Including Tokamaks and Planetary Magnetospheres (but, different… )

Levitated Dipole Experiment (LDX)! Princeton Large Torus (PLT)! ! ! 1.2 MA Superconducting Ring 17 MA Copper Toroid Steady-State 1 sec pulses 25 kW ECRH 750 kW Ohmic 1 MW ICRF (unused) 75 kW LHCD 2.5 MW NBI & 5 MW ICRF Outline

• Plasma containment depends upon the shape of the magnetic field

• What can we learn by changing magnetic topology? Examples…

• Stellarator: optimizing the helical plasma torus

• Levitated dipole: “simplest” axisymmetric magnetic confinement

• Spheromak: Magnetic self-organization

• Fusion energy needs discoveries to overcome challenges to economic viability

➡ Over 200 tokamaks and soon there will be ITER: what we know about the economics of tokamak-based fusion energy

➡ Discoveries are needed from creative new scientific investigations

• Columbia University’s plasma physics experiments More than 200 Tokamaks (We know how tokamaks work relatively well.)

ITER Significant Fusion Power already Produced in the Lab ✓ 2.5 MW/m3 achieved in TFTR! ✓ Establishes basic “scientific feasibility”, but power out < power in. ๏ Control instabilities, disruptions & transients ๏ Fusion self-heating, characteristic of a “burning plasma”, has yet to be explored. ๏ Steady state, maintainability, high-availability still T.B.D.

Fusion power development in the D-T campaigns of JET (full and dotted lines) ๏ The technologies needed for net and TFTR (dashed lines), in different regimes: power still T.B.D. (Ia) Hot-Ion Mode in limiter plasma; (Ib) Hot-ion H-Mode; (II) Optimized shear; and (III) Steady-state ELMY-H Modes. ITER: The International Burning Plasma Experiment

Built at fusion power scale, but without low-activation fusion materials, tritium breeding, …

~ 500 MW 10 minute pulses 23,000 tonne 51 GJ >30B $US (?) DIII-D ⇒ ITER ÷ 3.7 (50 times smaller volume) (400 times smaller energy) How to Design a Tokamak • Choose the shape of the magnetic plasma torus DIII-D • aspect ratio, ε = a/R ~ 0.16 b • elongation (shape), κ = b/a ~ 1.8

• Safety factor, q ~ 3 R a • Select operating parameters based on experience (high as possible)

• normalized plasma beta, βN ~ 1.8 (kink stability)

• normalized plasma density, nG ~ 0.85 (resistive stability)

• Select plasma temperature, (a B), β, and plasma current ⇒ • T ~ 0.6 × Ip ; choose T ~ 9 keV Ip = 15 MA and (a B) = 10 m ⋅T, and β ~ 2.5% 54 Divertor Segments (9 tons each) • Select magnetic field in superconductor (11.8 T) and shielding (1.4 m), determines size, plasma density, energy, and fusion power 20 -3 • R = 6.2 m, B = 5.3 T, n = 10 m , 400 MW fusion power, 350 MJ plasma energy, 50 GJ magnet energy, 0.9 GJ plasma current energy (enough to melt half ton of steel)

• Check plasma energy confinement needed to achieve desired fusion gain, Q ≡ (Power Out)/(Power In) ~ 10

• τE ~ 3.7 sec requiring only 40 MW of injected power (gyroBohm: Yes!!) and 120 MW power to divertor

2 • Check divertor cooling (must be less than 10 MW/m , ÷ 6 of surface of sun!) maybe? / maybe not?

• Check design and determine whether or not first wall survives plasma disruptions, ELMS, loss-of-control, …

• Check design and determine whether or not we can build it considering strength of materials, superconducting magnet technology, neutron radiation damage, current drive efficiency, …

• Figure out how to be tritium self-sufficient and become an affordable energy source… How to Design Bettera Tokamak • Choose the shape of the magnetic plasma torus DIII-D • aspect ratio, ε = a/R ~ 0.16 Optimize b • elongation (shape), κ = b/a ~ 1.8 Shape

• Safety factor, q ~ 3 R a • Select operating parameters based on experience (high as possible) Control

• normalized plasma beta, βN ~ 1.8 (kink stability) Instability

• normalized plasma density, nG ~ 0.85 (resistive stability)

• Select plasma temperature, (a B), β, and plasma current Better • T ~ 0.6 × I ; choose T ~ 9 keV ⇒ I = 15 MA and (a B) = 10 m ⋅T, and β ~ 2.5% p p Magnets 54 Divertor Segments (9 tons each) • Select magnetic field in superconductor (11.8 T) and shielding (1.4 m), determines size, plasma density, energy, and fusion power 20 -3 • R = 6.2 m, B = 5.3 T, n = 10 m , 400 MW fusion power, 350 MJ plasma energy, 50 GJ magnet energy, 0.9 GJ plasma current energy (enough to melt half ton of steel) Improve Confinement • Check plasma energy confinement needed to achieve desired fusion gain, Q ≡ (Power Out)/(Power In) ~ 10

• τE ~ 3.7 sec requiring only 40 MW of injected power (gyroBohm: Yes!!) and 120 MW power to divertor

2 • Check divertor cooling (must be less than 10 MW/m , ÷ 6 of surface of sun!) maybe? / maybe not?

• Check design and determine whether or not first wall survives plasma disruptions, ELMS, loss-of-control, … • Check design and determine whether or not we can build it considering strength of materials, superconducting magnet technology, Spread the neutron radiation damage, current drive efficiency, … Advanced Heat • Figure out how to be tritium self-sufficient and become an affordable energy source… Fuels Popular Science (May 2001) Popular Science (November 1981) Starfire Represented Optimism of early 1980’s

VACUUM PUMP SHIELD

WATER COOLANT INLET & OUTLET

BLANKET SECTOR

>:: f-'. f-'.

ANTI-TORQUE

13-·4059 Starfire: 1981 Charlie Baker, Mohamed Abdou, et al. (ANL) “Most detailed design to date of a year-2000 commercial fusion power reactor.” Two-year, $5.6 million study by ANL, McDonnell Douglas, and utilities Fig. 1. STARFIRE reference design - isometric view • • • • VACUUM PUMP SHIELD

WATER COOLANT INLET & OUTLET

30 m

BLANKET SECTOR

>:: f-'. f-'.

ANTI-TORQUE

13-·4059 Starfire ITER (1981) (> 2027) R, a (m) 7.0, 1.9 6.2, 2.0 Fig. 1. STARFIRE reference design - isometric view • I 10.1 15 B (T) 5.8 5.3 • • Duration continuous• 6000 x 7 min P 3510 410 P 1200 –250 Starfire = $5.7/We W 55 51 ! Tokamak (tonne) 24,000 23,000 ITER ≥ 35 × Starfire Cost ($M) 6,800 > 30,000 VACUUM PUMP SHIELD

WATER COOLANT INLET & OUTLET

30 m

BLANKET SECTOR

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ANTI-TORQUE

13-·4059 Starfire ITER (1981) (> 2027) Today’s 1st frontier for fusion… β 6.7, 7.3 2.5, 1.8 ! Fig. 1. STARFIRE reference design - isometric view • “to demonstrate the scientific and τ 3.6, 5.5 3.7, 1.0 technological feasibility of fusion n (10 1.0, 1.1 1.0, 0.85 •energy for peaceful purposes” • T (keV) • 24 9 Today’s 2nd frontier for fusion… λsol (mm) 100 ~ 1 ! Max Flux (MW/m 4 > 20 “the challenge is whether fusion can be done in a reliable, an economical, Neutrons (MW/m 3.6 0.6 and socially acceptable way” Material Low-Activation SS B-doped 316L ITER and advances in Alternate Energy Technology have made the issue of fusion’s cost unavoidable

• EIA (April 2013) Utility-scale Cost and Generation: ! Capital Cost 1984 2013 ! Fission: $5.5/W 37 GWy (96 units) 88 GWy (104 units) Solar PV: $3.9/W ! 0 2.5 GWy Solar Thermal: $5.1/W ! Onshore Wind: $2.2/W 0 16 GWy ! Offshore Wind: $6.2/W • Fusion research must address “economic viability” and show cost competitiveness • Holdren (Science, 1978): “Fusion, like solar energy, is not one possibility but many… The most attractive forms of fusion may require greater investment of time and money, but they are real reasons for wanting fusion at all.” Voids & bubbles in TMS

Adapted from Little, J. Nuc. Mater. 206 (1993) 324.

30 Simple solution treated austenitic steels: Fast reactor

9-13% Cr Martensitic steels: ~1%/dpa D-T20 Fusion’s MaterialsMixed spectrum reactor Challenge

~0.2%/dpa 316 SS Swelling, % “The development challenges for these materials9-13% systems Cr Martensitic pale 10 Simple ferritic alloys: by comparison to that for fusion materials, whichsteels: Fast is reactor arguably Fast reactor the greatest structural materials development challenge~0.01%/dpa in history. The combination of high temperatures, high radiation damage levels, intense0 production of transmutant elements (in particular, H and He)0 and high50 thermomechanical100 150 loads 200 that produce significant primary and Displacement secondary Dose, dpa stresses and time- dependent strains requires very high-performance materials for fusion energy systems. In contrast to first generation (late 1950s) demonstration fission reactor plants, where the maximum damage level achieved by any structural material was on the order of one displacement per atom (dpa), the structural materials in the first demonstration fusion reactor will be expected to satisfactorily operate up to damage levels approaching 100 dpa or higher.”

Advanced materials for fusion technology Steven J. Zinkle Fusion Engineering and Design, 74 (2005) p. 31-40 Two Pathways to Fusion Problem: Fast Neutrons

• Develop materials that withstand > 40 dpa/FPY & 10 He appm/DPA ! • Develop T breeding components ! ➡ Advance plasma confinement/ control to reduce cost

Problem: High plasma confinement

• Develop high field, high Tc superconductors ! ➡ Advance plasma confinement to achieve τp/τE < 1 at high beta Levitated Dipole may Make Possible Tritium Suppressed Fusion

Dipole T-suppressed fusion is an alternate technology pathway that avoids the need to develop breeding blankets and structural materials compatible with 14 MeV neutrons.

51 GJ 31 GJ WB ! 0.3GJ Wp 3 GJ ! 14 MeV Power >400 MW 14 MW Kesner, et al., NF (2004) Space Power Facility (SPF) Plum Brook Facility at Sandusky World’s Largest Vacuum Vessel ($190M & Nuclear Ready) Bigger than the ITER Cryostat

37 m

30 m Turbulent Pinch in a Levitated Dipole may Make Possible Tritium Suppressed Fusion

1024 • Sheffield, Zinkle, Sawan (2002-06)

• No tritium breeding blankets τp/τE = 1/5

No 14 MeV neutrons Q = 30 • 1023 • No structural materials problem Kesner • Requires τp/τE < 1 NF (2004)

• Requires 35 keV 1022 10 Q = 30 • Requires 10 fold confinement improvement τp/τE = 5

Requires stronger, higher-field ITER • 1021 superconducting magnets 0 25 50 75 T (keV) Turbulent Pinch in a Levitated Dipole may Make Possible Tritium Suppressed Fusion

(N, PδVγ) ~ constant implies peaked density and • Sheffield, Zinkle, Sawan (2002-06) pressure profiles (if γ > 1) • No tritium breeding blankets LSOL L • No 14 MeV neutrons 0 No structural materials problem • L*

4 • Requires τp/τE < 1 Cv ~ (Lsol/L0) • Requires 35 keV

Requires 10 fold confinement ΔSOL • CL improvement Adiabatic mixing implies • Requires stronger, higher-field core parameters determined by edge & superconducting magnets compressibility: γ-1 τe/τp ~ (4γ-3)Cv > 50 Dipole Proof of Performance Scaled from LDX to fit in NASA’s SPF

(a) ITER-Like D-T Tokamak Scaling (b) LDX-Like D-T Dipole Scaling 30 DEMO Q = 10 25 = 1 GPa σH 20 0.5 GPa Q = 10 15 ITER Q = 5 Q = 1 10 Q = 1

5 JET reduced alpha confinement LDX: 1.5 MA/0.33 m

Plasma Radius (m) Conductor Radius (m)

Fusion Gain - Magnet Stress - Quench Safety Parameter - Alpha Confinement Summary • Plasma containment and the success of fusion energy research requires understanding how best to shape the magnetized plasma torus • Fusion researchers must make discoveries to overcome challenges to economic viability

Fusion Stellarator Starts Up An Interview With Linus Torvalds, Alternate design to ITER might ultimately be better Creator of Linux for generating electricity By Dylan Love By Alexander Hellemans BUSINESS INSIDER Posted 21 May 2014 | 19:44 GMT ANALYZING THE TOP NEWS STORIES ACROSS THE WEB JUNE 9 2014 10:00 AM But ITER? With a huge, complex, expensive piece of hardware that you'll have one (or eventually just a handful) of? Yeah, I'm going to go out on a limb and say that there's a lot of red tape and politics and bureaucracy, to the point where collaboration is going to be really hard. A lot of committees... There's a lot of people hoping for a simpler, smaller, and yes, more scalable solution.