Session 2: DEMO Physics Gaps and

Impact on Engineering Design

Introduction

Hartmut Zohm

Max-Planck-Institut für Plasmaphysik

Boltzmannstr. 2, D-85748 Garching, Germany

Presented at 4th IAEA DEMO Workshop, KIT, Germany, 16.11.2016

The Fusion Plasma – Physicist’s View

A highly nonlinear system far away from thermodynamic equilibrium

The Fusion Plasma – Engineer’s View

An object in the centre of a power plant defining the loading conditions

Main design parameters of the machine:

• vacuum vessel: major radius R, aspect ratio A, shape

• toroidal and poloidal magnetic field coil system Bt, Bp (tokamak: Ip)

• auxiliary heating and current drive power PCD

• fuelling and pumping requirements (gas fluxes)

Output parameters

• fusion power and ‚plasma Q‘: Pfus = Q PCD

• thermal loading conditions

• pulse length tpulse and duty cycle (tokamak issue)

• mechanical loading conditions

Design rules link design parameters and output

parameters

Note: on this level, no distinction made between tokamak and stellarator

Design rules – very simplistic version

In the optimum temperature range, fusion power is proportional to p2V:

with

In tokamaks, MHD instabilities set a limit to (Troyon-Limit)

so that

(note safety factor q95 ~ aB/(A Ip) )

Simple scaling for fusion power

42

95

342

1Aq

RBcP N

fus

𝛽𝑁 =𝛽

𝐼(𝑎𝐵)

2

342

1~

A

RBcPfus

𝛽 =

𝑛𝑇

𝐵2

(2𝜇0)

Loss power from plasma W/tE expressed through scaling law for tE:

tokamak: ITER98(p,y2)

stellarator: ISS04

Insert this into the power balance

tokamak:

stellarator:

• strongly nonlinear in R, i.e. will define ‚minimum size‘

• high H-factor (good confinement) and low q95 (high Ip) help a lot!

Simple scaling for ignition

...*~ 73.039.07.023.3 AqH BohmE tt

15

5

5

17.37.21.023.3

53.31.3

1

2

BRH

Aq

c

cPP

P

P

PQ

N

fusloss

fus

AUX

fus

...*~ 0.006.119.079.052.2 AqH BohmE

tt

1~

~5

5

5

179.379.281.056.2

79.206.1

1

2

BRH

Aq

c

cPP

P

P

PQ

fusloss

fus

AUX

fus

Evaluating c1 and c2 from ITER Q=10 * / HELIAS Option A**, one gets

• i.e. ignition at a minimum size of R = 7.5 m / 15.5 m, respectively

• above, tokamak Q determined by PCD, stellarator practicallly ignited

*(A=3.1, R=6.2 m, Bt=5.2 T, q95=3.1, H=1, N=1.8, Q=10, Pfus=400 MW, Ploss=120 MW)

**(A=10.5, R=14 m, Bt=4.5 T, q=1, H=1.8, =4.3, Q=10, Pfus=500 MW, Ploss=150 MW

according to F. Warmer et al., Plasma Phys. Control. Fusion 2016)

Simple scaling for ignition

Total solenoid flux Ftot consumed by ramp-up F0 and flat top Fres

The flux consumed in flattop is given by

where

fCD = fraction of externally driven current

fbs = fraction of bootstrap current

Pulse length can now be derived from the flux balance

• yields a ‚resonance denominator‘ (singularity = steady state)

• note: as for Pfus, N helps, but now q95 should be as high as possible!

Simple scaling law for tokamak pulse length

restot FFF 0

)1(95

5 bsCDt

pulseres ffq

Bc F t

)7.01(

)(

9565

095

NCD

totpulse

AqcfBc

q

t

FF

Total solenoid flux Ftot consumed by ramp-up F0 and flat top Fres

The flux consumed in flattop is given by

where

fCD = fraction of externally driven current

fbs = fraction of bootstrap current

Pulse length can now be derived from the flux balance

• yields a ‚resonance denominator‘ (singularity = steady state)

• note: as for Pfus, N helps, but now q95 should be as high as possible!

Simple scaling law for tokamak pulse length

restot FFF 0

)1(95

5 bsCDt

pulseres ffq

Bc F t

)7.01(

)(

9565

095

NCD

totpulse

AqcfBc

q

t

FF

bootstrap current

jbs ~ p/Bpol

fbs ~ q95 A N

ITER Q=10 scenario* ITER Q=5 scenario**

low q95 (maximum Ip) high q95 and H (maximum fbs)

high fusion power (Q=10) lower fusion power (Q=5)

pulsed (400 s) steady state

Typical trade-off in advanced tokamak scenarios: increase q, compensate

with improved confinement (higher H)

*(A=3.1, R=6.2 m, Bt=5.2 T, q95=3.1, N=1.8, fCD=0.1, Ftot=120 Wb, F0=90 Wb, tpulse=400 s)

**(A=3.3, q95=5.1, N=2.5, fCD=0.5, H=1.5)

Tokamak pulse length: the problem of steady state

Psep

Additional constraints from power exhaust

4/5 of Pfus in neutrons, load the wall at ~1 MW /m2

1/5 of Pfus in charged particles, load narrow

ring in the divertor, potentially damaging

• limit power flux across separatrix to

Psep = fLH PLH (H-mode power threshold)

• can be achieved by seed impurity radiation,

but must not compromise core performance

• establish ‘detached’ divertor solution

(PFCs protected by ‘cushion’ of neutrals)

• relevant dissipative processes (radiation,

charge exchange…) all need high density

Exhaust constraints tend to impact core

• core impurity seeding may cool and dilute plasma core

• high density difficult to achieve in large device (nGW ~ B/(q95R))

If it is that simple, why this session?

There are considerable uncertainties in several of the relations used

• scaling laws for tE and PLH are empirical with little physics basis

• scaling laws have been derived for ITER, not DEMO conditions (DEMO

will have higher , higher n/nGW, higher frad)

• stability limits depend on plasma profiles and hence in principle need

sophisticated control if operating close to them

• divertor detachment cannot be predicted quantitatively today

This session focuses on these uncertainties (= knowledge gaps) and how

we intend to close them

• uncertainties in core physics (R. Hawryluk) and exhaust (H. Reimerdes)

• additional constraints arising from scenario integration (V. Chan)

• effect of uncertainties on the final outcome / design margins (H. Lux)

• status of stellarator knowledge base (J. Miyazawa)