Session 2: DEMO Physics Gaps and Impact on Engineering ......Session 2: DEMO Physics Gaps and Impact...
Transcript of Session 2: DEMO Physics Gaps and Impact on Engineering ......Session 2: DEMO Physics Gaps and Impact...
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)