Conceptual design of an energy recovering

divertor

Derek Baver

Lodestar Research Corporation

Conceptual design of an energy recovering divertor, D. A. Baver, Lodestar Research Corporation.

Managing divertor heat flux is a key issue in the design of ITER and a critical issue in the design of DEMO, with current projections suggesting materials limitations in the latter case. One approach to this problem is to adapt the concept of plasma direct convertors (PDC’s) to the tokamak geometry. PDC’s, a technology originally developed for the mirror reactor concept, convert plasma thermal energy into electricity with extraordinarily high efficiencies, in some cases exceeding 80%. Converting thermal energy into electricity simultaneously solves two problems, on one hand reducing heat load to the divertor by converting energy into non-thermal form, and on the other hand providing a source of recycled power for profile control, thus reducing dependence on bootstrap current. Unfortunately, most PDC designs require a magnetic expander, which is impractical in a tokamak geometry. Removing the magnetic expander results in a high density, high magnetic field regime. The former limits the effects of electrodes due to Debye screening, whereas the latter results in beta too low for MHD generation schemes. We will discuss several approaches to extracting useful work in this regime, employing such effects as ponderomotive force and particle drifts.

Work supported by the U.S. DOE under grant DE-FG02-97ER54392.

Outline

• What is an ERD?

• Motivation

• Background

• Effects on energy balance

• Issues

• Solutions– Pitched biased plates

– Counterrotating waves

– Retrograde scrape-off

• Conclusions

What is an ERD?• An energy recovering divertor (ERD) is a

plasma direct convertor (PDC) that is specifically designed to work with tokamak divertor plasma.

• PDC’s convert plasma thermal energy into electricity.– Multi-electrode design is common on

mirror machines.– Efficiencies over 80% reported in some

cases.• ERD’s require different principles than

PDC’s used on mirrors.– High density, low magnetic expansion

renders multi-electrode design impractical.

– Strong toroidal field necessitates PDC construction inside reactor vessel rather than as a separate device.

• Designs proposed here satisfy these conditions.

Motivation• Divertor heat flux problem:

– Current calculations suggest challenging divertor heat fluxes for ITER, DEMO• 10-20 MW/m2 for ITER

– Careful design pushes against materials constraints.

• 30-40 MW/m2 for DEMO– Exceeds current materials constraints.

– Reduced heat flux necessary for viable reactor

– Current approaches emphasize spreading out heat• Snowflake divertor• Super-X divertor

– Alternate approach: prevent heat from reaching the divertor plate• Electric power does not count towards

thermal flux• Some ERD designs spread out waste heat as a

side effect

• Plasma direct conversion potential:– Direct conversion radically changes

reactor energy balance.• Increases overall reactor efficiency• Provides source of recycled power for current

drive, profile control, etc.• Significant even for D-T because recycled

power counts towards charged particle energy– Energy can be re-recycled– Can significantly alter Lawson criterion

– Existing PDC research concentrates on magnetic mirrors• Bundle divertor makes PDC easy to install on

mirror machines• Originally conceived as a way to save the

mirror program– PDC potential more appropriate for

Tokamaks• Mainline reactor concept• Closer to breakeven

– Modest adjustment to Lawson criterion allows breakeven reactor based on existing experiments.

• An ERD accomplishes both of these.

Background• PDC’s are devices to convert plasma heat

into electricity.– Originally developed for mirror machines.– Plasma escaping one end of the mirror passes

through a magnetic expander.• Converts perpendicular velocity into parallel

velocity.• Reduces density.

– A grid separates charged particle species.– One species passes a series of charged plates.

• Electric field around plates focuses particles with sufficient energy to pass.

• Reflected particles defocus and hit plates.• Particles are sorted by energy so that thermal

kinetic energy is converted into electrical potential energy.

– Very high efficiencies reported in experiments.• Cuspec: 70%• Moir-Barr-Carlson: 86%

A simple one-stage PDC with conical magnetic expander.*

A 22-stage PDC with ion trajectories inside focusing and collecting system.*

*from Direct Energy Conversion in Fusion Reactors, Ralph W. Moir, Energy Technology Handbook.

Effects on energy balance• PDC’s have greatest effect when advanced fuels are used.

– Improved efficiency for charged particles only.– Only 20% of power is in charged particles for D-T

• However, effect on D-T is not trivial.– Injected power counts towards charged particle total.– Possibility of high recycled power operation.

• Define parameters:– Q= Pfus/Ph gain– QL= fchPfus/PL fraction of Lawson criterion

• Then assuming 70% heating efficiency, 40% steam efficiency, and complete recycling of ERD/PDC power, breakeven parameters are affected as follows:

NoPDC/ERD

50% efficientPDC/ERD

80% efficient PDC/ERD

Breakeven (steamRPF=100%)

QL = .472Q = 4.47

QL = .307Q = 2.22

QL = .208Q = 1.31

Economical operation (steamRPF=20%)

QL = .817Q = 22.3

QL = .531 Q = 5.66

QL = .359 Q = 2.80

“Ignition” (steam RPF=0%)

QL = 1Q = inf.

QL = .65 Q = 9.29

QL = .44 Q = 3.93

Plasma heating system

Steamgenerator

ERD

Core heat

Edge heat

High-grade heat

Electricity

Fusion burn

Low-grade (waste) heat

Neutrons

Transport

Charged particlesDeliveredheat

Injectionloss

Conv

ersi

on lo

ss

Oth

er lo

ss

Power out

Electrode heating

Radiative loss

Red indicates dominant path for recycled power

Energy flowchart for fusion reactor with ERD

Issues• Tokamak PDC can’t be in external chamber as

with mirror PDC.– Toroidal field coils completely surround plasma.– Threading flux bundles between TF coils requires

high localized curvature.• High mechanical stress• High current density• Strong non-axisymmetric field

• No external device means no magnetic expander.– Presence of strong toroidal field limits B ratio to

toroidal field ratio.– Variation in toroidal field is small compared to

conventional PDC requirements.• No magnetic expander limits use of electrodes.

– Divertor plasma retains high density if magnetic expansion is small.

– High density results in small Debye length.– Small Debye length means external electric fields

fail to penetrate plasma.• Steady parallel fields vanish.• Only perpendicular or oscillating fields remain.

• This necessitates an entirely different approach to extracting power from the plasma.

Solution 1: Pitched biased plates

• Divide pitched divertor into separately biased segments.

• Ions will strike earlier segments than electrons.– Finite Larmor radius allows ions to strike plate

close to field line.– Electrons continue along field lines.– Resulting charge separation extracts free energy.

• ExB drift from bias partially cancels perpendicular ion velocity.– Ions impact divertor with less energy.

• Theoretical efficiency as high as 78%.– Assuming Gaussian distribution, offset to velocity

reduces average impact energy.• But this applies only to perpendicular ion velocity.

– Actual maximum efficiency only 26%.• Poor by itself, but combines well with other

approaches.– Other approaches conver parallel velocity more

easily.– Other approaches can harness electron energy.

Solution 2: Counterrotating waves

• An antenna launches two slow-branch Alfven waves in opposite directions.

• Superposition of these waves results in ponderomotive bunching of the background plasma.

• Density variations result in parametric reflection.

• The wave moving parallel to plasma streaming is absorbed by the antenna, and part of the energy used to reinforce the other wave.

• Blueshift from plasma motion adds energy to the absorbed wave, so that net energy is removed from the plasma.

Overall layout of spherical tokamak withERD based on counterrotating wave principles. Color is for clarity to distinguishflux surfaces.

• Power harnessed by interaction between antenna and waves.– Waves allow antenna to “grip” plasma.– Analogous to plasma “cog.”– Reliance on recirculated power means RF systems must

be efficient.• Counterrotating wave approach only harnesses

parallel velocity.– Requires magnetic expansion to convert perpendicular

to parallel.• Magnetic expansion based on aspect ratio.

– Favors spherical tokamaks.– If expansion ratio ~2, maximum efficiency is ~66%.– Some electron perpendicular energy may be harnessed

due to collisional equilibriation of perpendicular and parallel temperature.

• Does not spread out plasma.– Plasma must expand to create net thrust to drive

rotating waves.• Perpendicular expansion does not occur in wave region due to

narrow frequency band of slow Alfven waves.– This is accomplished by increasing phase velocity of

beat wave.• Typical geometries limit this to ~1.4, yielding 50% energy

recovery.– Beat wave must slow again to recover bulk parallel

velocity.– Net energy is absorbed because plasma is cooler when

it recompresses.• Radiative losses.• Electron conduction losses.• Neutral collisions.

Solution 3: Retrograde scrape-off

• Variant on counterrotating wave approach with potential for large efficiency gains.

• Reflection of ions by ponderomotive force results in banana orbits.

• If divertor plate is highly pitched, ions will strike from one side of banana orbit.– Creates correlation between direction of

parallel velocity and position.• Appropriately oriented divertor plate

will collect particles moving opposite bulk plasma flow.– Residual kinetic energy greatly reduced.– Creates reaction thrust that acts on beat

wave.• Need for velocity change in beat wave

obviated.– Improvement in efficiency is scalable

based on pitch angle of divertor plate.

Potential issues:• Requires waves to be close to

divertor plate.– Waves may be absorbed.– Ponderomotive potential may null at

surface.• Only directly affects ions.

– Electrons indirectly affected due to gradual unloading of bunches.

– Electrons must rely on evaporative cooling vs. plasma potential.

Conclusions• Multiple methods may be used to convert plasma

thermal energy in the divertor channel into electricity.– Plasma waves convert thermal energy to RF.– Biased electrodes convert thermal energy to DC.

• Methods may be combined to achieve higher efficiency.

• Methods work well with techiques to spread out heat flux.– Combination gives compound heat flux reduction.

• This also provides additional power from the plasma.– Auxiliary power for heating, current drive.– Or just put the extra power onto the grid.

• Efficient power recycling makes ignition easier.– JET/JT60 behaves like ITER, ITER behaves like

DEMO.• Current approaches most effective at extracting

ion energy.– Disproportionate reduction in divertor sputtering.

• Further research needed to optimize this approach.– Existing approaches need further investigation and

design work.– Numerous additional approaches are possible.