Who will save the tokamak Harry Potter Arnold

Who will save the tokamak – Harry Potter, Arnold Schwarzenegger, Shaquille O’Neal or Donald Trump? J. P. Freidberg, F. Mangiarotti, J. Minervini MIT Plasma Science and Fusion Center PPPL Jan. 20 , 2015 1

Why does the tokamak need saving? • Standard tokamak does not scale to a reactor • Design determined almost entirely by nuclear physics and engineering constraints • One piece of plasma physics enters the design – empirical • The plasma physics is not up to the task 2

How can I prove this? • Design a tokamak reactor from an engineering view • Use only plasma physics • Obtain reasonable values for all engineering parameters • Obtain reasonable values for all plasma parameters • More important – give a non-plasma physics reason for choosing each parameter • Test design against known tokamak operational limits • The design FAILS 3

The approach • Use simple models • No pretense of high precision • Show there is one possible show stopper • Discuss 4 strategies to solve the problem • Many of you are aware of the key results • How we get there is what is interesting • Let the design begin 4

ARIES Tokamak Reactor 5

Theoretical approximation 6

Goals of the design Quantity Symbol Minor radius of the plasma Major radius of the plasma Elongation Thickness of the blanket region Thickness of the TF magnets Average plasma temperature Average plasma pressure Average plasma density Energy confinement time Magnetic field at Normalized plasma pressure Plasma current Bootstrap fraction 7

Nuclear Physics Constraints • Neutron slowing down: • Tritium breeding: • D-T Fusion: 8

Engineering constraints 1 Steady state ignited reactor • Electric power out: • Neutron wall loading: • Recirculating power fraction: • Thermal conversion efficiency: 9

Engineering constraints 2 Superconducting niobium-tin magnets • Maximum field at the coil: • Maximum mechanical stress: • Maximum current density: • Wall to RF conversion efficiency: 10

Analysis strategy • Use the constraints to express all parameters in terms of • Define a reference case: • No justification for reference case – just an example • Examine design as a function of • Show no value of works: identify show-stopper • Examine 4 possible solutions 11

Ellipticity • • Not very controversial Good for plasma physics: increased and Good for engineering: lower But there are limits Plasma limit – vertical instabilities Engineering limit – feedback control design We choose 12

First wall, Blanket, Shield, Vac. Ch. b Plasma First wall Blanket Shield Vac. Ch. 13

Focus on the Blanket • Blanket thickness from nuclear physics constraints • Use conservation of mass and energy 14

Blanket (cont. ) • Calculate to reduce neutron flux to • Add some shield, first wall, and vacuum chamber, improve optimization • We choose 15

Neutron Wall Loading Relation between R 0 and a • Wall loading relation 16

Solve for R 0 • Solution • Reference case: • Then 17

Magnetic field at R = R 0 • A good approximation: • Then • For the reference case 18

TF Coil Design Relation between c and a • Coil thickness = structure + superconductor • Structure - Magnet forces • Tensile forces • Centering forces • Overturning forces small - neglect 19

Tensile force balance • Tensile forces • Solve for the tensile stress 20

Centering force balance • Centering forces • Solve for the compression stress 21

Stress thickness • Tresca Stress = Maximum stress • Solve for stress thickness 22

SC current density thickness • How much SC is needed to carry TF current? • Solve for 23

Total coil thickness • Total = sum of tensile plus centering • For the reference case 24

Plasma temperature • Assume • Fusion power density • Choose to maximize 25

Plasma pressure • Thermal power must produce desired output power • Simple “vanilla” profiles 26

Plasma Pressure (cont. ) • Cross section • Volume element • Solve for • For the reference case 27

Plasma beta • From the definition • For the reference case 28

Plasma density • Density from • For the reference case 29

Energy confinement time • Ignited operation: alpha power = thermal conduction losses • Solve for • For the reference case 30

The plasma current • Here is where plasma physics enters • Empirical ELMy H-mode scaling • Solve for the current • For the reference case 31

The kink safety factor • From the definition • For the reference case 32

Bootstrap fraction • From recirculating power fraction and CD efficiency • Assume Lower Hybrid current drive – outside launch • Recirculating power fraction • Electrical conversion efficiency 33

Bootstrap fraction (cont. ) • Current drive • For the reference case • The bootstrap fraction 34

Two additional figures of merit • Cost: • Reference case • Heat flux: • Reference case 35

How well does the plasma shape up? • Test the plasma against 4 plasma limits • Greenwald density limit • Troyon beta limit • Kink safety factor limit • Achievable bootstrap fraction 36

Greenwald density limit • Density limit • Reference case 37

Troyon beta limit • Beta limit • Reference case 38

Kink safety factor limit • Safety factor limit • Reference case 39

Bootstrap fraction limit • The maximum bootstrap fraction: • Model for the total 40

Total current density profile 41

Bootstrap fraction limit (cont. ) • The neoclassical bootstrap fraction • The bootstrap limit • For the reference case 42

The basic problem • • • Too much current is needed for ignition Yes but we assumed that Maybe there is a better value for ? Let’s see! Plot • All must simultaneously be less than 1 for success 43

No value of works!! 44

What’s the consequence? • Without steady-state the tokamak is on the path to nowhere SHOW STOPPER 45

What should we do about it? Four possible solutions • The Harry Potter solution • The Arnold Schwarzenegger solution • The Shaquille O’Neal solution • The Donald Trump solution 46

The Harry Potter Solution Advanced Plasma Physics • Raise , set to fix • Lowers the required I • Lowers the achievable n • Lowers the achievable • Still violates limit • Success requires 47

Plasma Physics Strategy - Magic

The Arnold Schwarzenegger Solution Advanced Magnet Technology • Raise , set to fix • Improves plasma physics • Raises • Success requires 49

Engineering Strategy – Strong B 50

The Shaquille O’Neal Solution Economy of Scale • Raise , set to fix • Keep standard • Economy of scale benefits • Leads to a larger plant • About the same • Success requires 51

Utility Risk – Large Power Plant 52

The Donald Trump Solution Easier Engineering • • • Lower , set to fix Keep standard Eases engineering A large, expensive plant Much larger Success requires 53

Economic Risk – Large $/W 54

What if the tokamak doesn’t work? There is always the stellarator 55

Our opinion • Donald Trump: Not attractive economically • Shaquille O’Neal: Not attractive utility-wise • Harry Potter: May work, but risky if only option • Arnold Schwarzenegger: Best new hope because of game changing technology 56

Some observations • Some say plasma physics is done – we should focus on engineering • We do not agree! • Do not know how to make a steady state tokamak at high • No solution yet for heat load problem – not primarily a materials problem, but a divertor problem • Designs tend towards larger • Plasma performance improves at high 57

The US Fusion Program • What elements should be included? • How well are they supported on a scale of 10? • Advanced tokamak physics 8 • Steady state high performance plasma 6 • Stellarator research 3 • Advanced magnet technology 1 • Fusion-fission hybrids 1 58

Can we improve the US Program? • We have a chance • Community input mandated by Congress • Charge and procedures very important • Don’t need a charge by Machiavelli and Madoff They can’t be trusted! • Do need a charge by Maxwell and Newton They can’t be fooled! 59