The most investigated magnetic fusion configurations … Euratom-ENEA sulla Fusione PROTO-SPHERA Workshop, Frascati, 18-19/3/2002 C. Alessandrini, F. Alladio, G. Apruzzese, G. Bracco,

Associazione Euratom-ENEA sulla Fusione PROTO-SPHERA Workshop, Frascati, 18-19/3/2002

C. Alessandrini, F. Alladio, G. Apruzzese, G. Bracco, L. Bettinali, P. Buratti,A. Coletti, P. Costa, C. Crescenzi, A. Cucchiaro,

R. De Angelis, T. Fortunato, D. Frigione, M. Gasparotto, G. Gatti, R. Giovagnoli, L.A. Grosso, G. Maddaluno, G. Maffia, A. Mancuso,

S. Mantovani, P. Micozzi, S. Migliori, G. Monari, C. Nardi, S. Papastergiou, S. Pierattini, L. Pieroni, M. Pillon, A. Pizzuto,

M. Roccella, F. Rogier, M. Santinelli, L. Semeraro, A. Sibio, B. Tilia, O. Tudisco, L. Zannelli, V. Zanza

2

OUTLINE

• PURPOSE • HELICITY INJECTION • PHYSICAL DESIGN • COST, SCHEDULE & SIZE

PROTO-SPHERA Workshop, Frascati, 18-19/3/2002 Associazione Euratom-ENEA sulla Fusione

• REACTOR EXTRAPOLATION: CKF CONFIGURATIONS

PURPOSE

3

PROTO-SPHERA (Spherical Plasma for Helicity Relaxation Assessment) aims at producing a spherical torus (ST) with a screw pinch (SP) replacing the centerpost

Relaxed state, ��

��

=��

��

�

��

B��

B , with ��constant all over the plasma, enclosed within a perfectly conducting portion of sphere, with radius Rsph, fed by two electrodes upon the polar caps

"Flux-Core-Spheromak" "Spheromak"


Ideal MHD Stable ��|�� Ideal MHD Unstable

PURPOSE

4

The most investigated magnetic fusion configurations are not simply connected: A central post links the plasma torus

The feasibility of simply connected, fusion relevant, magnetic configuration would strongly simplify the design of a fusion reactor

A simply connected configuration is also more suitable for channeling particle jets and

transforming fusion power into propulsive power (for space thrusters)


PURPOSE

5

Compact Tori yield simply connected plasma configurations: Spheromaks and FRC’s


They have up to now been less successful than ST as they rely more heavily upon plasma self-organization, both for their formation as well as for their sustainment Although many formation schemes have produced in the last twenty years interesting Spheromaks and Field Reversed Configurations (FRC), at the present moment no sustainment scheme has been soundly and fully demonstrated

PURPOSE

6

Spheromaks are usually formed by magnetized coaxial plasma guns used as helicity injectors, in presence of a close conducting shell


Breakdown in small spaces, with extremely high filling pressures and kV voltages � Big amount of neutrals and impurities are released from the gun After the formation, the Spheromak is accelerated and expanded into a flux conserver � Field errors already present in the gun are amplified PROTO-SPHERA will form instead at tokamak-like densities, with very low voltages (~100 V) and will not undergo any expansion

PURPOSE

7

Flux-Core-Spheromak obtained on the TS-3 experiment (University of Tokyo, 1993) Filling gas (pH~2•10-2 mbar); break-down (Ve~1 kV) using two plasma guns as electrodes Screw pinch current increases: toroidal plasma formation, non-linear kink: qPinch<1÷2


Compression coils pulsed � flux swing has driven much of toroidal plasma current

After formation (~60 �s), the TS-3 configuration was sustained for 20 �sec, i.e. 30•�A PROTO-SPHERA aims at sustaining the toroidal plasma through DC helicity injection

HELICITY INJECTION

8


• The plasma with open field lines (intersecting electrodes) has �~0, therefore

�

��

�

j ||�

��

B • Because of the twist of the open field lines, the current between the electrodes also winds in the toroidal direction near the closed magnetic flux surfaces • Resistive MHD instabilities convert, through magnetic reconnections, open current/field lines into closed current/field lines, winding on the closed magnetic flux surfaces • Magnetic reconnections necessarily break, through helical perturbations, the axial symmetry, as per Cowling's anti-dynamo theorem

HELICITY INJECTION

9

For a simply connected volume bounded by a magnetic surface (�

��

B • =0): A

ˆ nBK=�

��

•��

��

dV, magnetic helicity, is a slowly decaying ideal MHD invariant and measures how much the lines of force are interlinked, kinked or twisted

Any initial configuration will self organize in a relaxed state �

��

��

��

B =��

��

B , with �=�0

��

��

j •�

��

B /B2= constant all over the plasma, after sufficient time (Taylor's assumption) For a volume not bounded by a magnetic surface � relative magnetic helicity


�K = �Va�

��

A +��

A V��

��

��

��

B -��

B V��

��

�� dV

This choice uses the vacuum potential field in Va, ��

B a'=��

��

B V which obeys in Va:

��

��B ��

��

��

V=0, with �

��

B V• ˆ n a= �

��

B a• ˆ n a, and is assigned zero helicity

HELICITY INJECTION

10

A domain containing magnetized plasma, with open field lines passing through the boundary, offers the opportunity of refurbishing the helicity content of the plasma

"Poynting's theorem" for the relative magnetic helicity in a domain, ( points outwards), d(�K)/dt = - 2��

ˆ nE��

B • ˆ dS - 2��n�

��

A ��

��

A /�t• ˆ dS - 2� (n�

��

E •B ) dV , where • 2��

��

��

E �

��

B • ˆ dS = DC helicity injection� �n E electrostatic potential • 2��

�

��

A ��

��

A /�t• ˆ dS =AC helicity injection; nincludes the inductive helicity injection (ohmic) 2Vloop�T;

• 2� (�

��

E •�

��

B ) dV total helicity dissipation


Injection rate: |d(�K)/dt|=2Ve�e, Ve electrostatic potential �e=0.5 ��

�

��

B • ˆ | dS magnetic flux

Magnetic flux, plasma current and magnetic energy injected along with the magnetic helicity

n

HELICITY INJECTION

11

Reconnection processes convert part of the magnetic energy into kinetic energy of the magnetized plasma, HIT Washington University (Seattle)

Energy efficiency (from HIT results) �=IpVloop/IinjVinj=0.25


HELICITY INJECTION

12

If helicity source (SP of PROTO-SPHERA) is physically separated from helicity sink (ST of PROTO-SPHERA) a gradient in the relaxation parameter (

�

��

��≠0) appears: resistive MHD instabilities produce helicity flow from larger � to smaller � regions

d(�K)/dt = - ��- ��• dS - 2��

�

��

��

� ˆ n E �

��

B • dS - 2��ˆ n�

��

A ��

��

A /�t• dS - 2� (ˆ n�

��

E •�

��

B ) dV • -

�

��

�(��

��

j •�

��

B /B2))=- �� helicity flux (Boozer fluctuation-averaged Ohm's law) ��

��

��

SPHEX at UMIST (Manchester) has explored �� in a Flux-Core-Spheromak ��

��

�


In agreement with the results of SPHEX, the PROTO-SPHERA equilibria have been calculated in order to get: 2.4 ≤�Pinch/<�ST>(axis) ≤ 3.3

PHYSICS DESIGN

13


Ie, Ip = 40, 50 kA pinch, ST currents I e, Ip = 60, 240 kA A = 1.6 aspect ratio A ≤ 1.3 �pulse = 80 �s~110 �A pulse duration �pulse ≥ 70 ms~1 �R

• PROTO-SPHERA has separate electrodes chambers containing disk shaped plasmas • PROTO-SPHERA aims at sustaining the plasma for more than �R=�0a2/� (resistive time)

PHYSICS DESIGN

14

• PROTO-SPHERA aims at a prolate ST elongated �~2.3, to get q0~1 and q95~2.5÷3 In PROTO-SPHERA (Rsph=0.35 m) the structure of the fields has been designed in order to be as far as possible from the pure Spheromak �STRsph≤4.2, and in order to get profiles with q0~1 and q95~2.5÷3


PHYSICS DESIGN 15

ST diameter 2•Rsph=0.7m


Toroidal plasma current Ip=240kA Aspect ratio A=1.2, elongation �=2.35

Similar to the START spherical torus experiment Pinch current Ie=60 kA « Itf≈200 kA (START centerpost)

PHYSICS DESIGN

16

Main constraint designing PROTO-SPHERA: current density within the plasma

Plasma-cathode interface: je=100 A/cm2 on electrode's testbench PROTO-PINCH


In PROTO-SPHERA requirement of 3 rows of filaments reduces the limit to je~80 A/cm2 Ribbon with radius Rel=0.4 m and width �Z~3.0 cm, limits Ie=2�Rel�Z•je~60 kA

PHYSICS DESIGN

17

Two groups of PF coils (jPF≤2 kA/cm2), each composed by coils connected in series

Group 'B' - shape the pinch with constant currents


Group 'A' - compress the ST with variable currents

PHYSICS DESIGN 18

Screw pinch (SP) formed by a hot cathode breakdown • Filling pressure pH~10-3÷10-2 mbar • Cathode filaments heated to 2600 °C • Ve~100 V applied on the anode • Electrode arc current limited to Ie~8.5 kA


PHYSICS DESIGN

19

PROTO-SPHERA formation time: TS-3 took 80 �s to reach Ip/Ie=1.2 Scaling up as S1/2

�A (Sweet-Parker reconnection) and including all passive currents:

t= t0-100�s t= t0+300�s t= t0+600�s t= t0+1 ms Ie=8.5 kA Ie=45 kA Ie=54 kA Ie=60 kA


Ip=0 kA Ip=30 kA Ip=60 kA Ip=120 kA

PHYSICS DESIGN

20

Although finite amplitude resistive MHD instabilities are required to inject helicity from the pinch to the ST, the combined configuration must be ideal MHD stable New finite element method ideal MHD stability codes have been developed in order to analyze the combined screw pinch + spherical torus configuration of PROTO-SPHERA

The ideal MHD stability limits to the ratio Ip/ Ie, depending upon �ST=2�0<p>ST/<B2>ST With �ST~30% Ip can reach a value of 1•Ie With �ST~20% Ip can reach a value of 2÷3•Ie


With �ST~10% Ip can reach a value of 4•Ie (design limit)

COST, SCHEDULE & SIZE 21

COSTS Vessel, including: tiles, supports, baking system and base 665,000 Euro Design contract 77,000 Euro Subtotal 742,000 Euro

Poloidal field coils, including : feedthroughs and cooling system 826,000 Euro Design contract 77,000 Euro Subtotal 903,000 Euro

Anode and Cathode, including feedthroughs and cooling system 297,000 Euro Design contract 50,000 Euro Subtotal 347,000 Euro

Assembly contract 90,000 Euro

Pumps, gas feed & control system 200,000 Euro

TOTAL 2,282,000 Euro

Power supply: Pinch feeder ‘P’ 904,000 Euro Cathode feeder ‘K’ 102,000 Euro PF feeder ‘A’ 150,000 Euro PF feeder ‘B’ 31,000 Euro Subtotal 1,187,000 Euro Electrical work contract 93,000 Euro

TOTAL 1,280,000 Euro


GRAND TOTAL 3,562,000 Euro

COST, SCHEDULE & SIZE

22

TIME SCHEDULE TOTALS Year 1 Year 2 Year 3 Year 4

LOAD ASSEMBLY Design Contract Tender Construction Check Assembly Final check Guarantee ASSEMBLY WORK Tender Orders Work Final check PUMP,GAS,CNTRL Tender Orders Assembly Final check PF COILS Design Contract Tender Construction Check Assembly Final check Guarantee ELECTRODES Design Contract Tender Construction Check Assembly Check Final check Guarantee POWER SUPPLY Design Tender Construction Check Check Assembly Final check Guarantee ELECTRICAL WRK Design Tender Work Final check Guarantee


COST, SCHEDULE & SIZE

23

PROTO-SPHERA has as almost the same size of START Also the performances are predicted very similar to the ohmic results of START �Formation~1 ms, <Te>=140 eV, �E

LG~1.6 ms and �R~70 ms at <ne>=5.0•1019 m-3, A possible reduction of the size of PROTO-SPHERA should be operated while keeping constant all the current densities (in the plasma as well as in the conductors): A reduction by 1.66 would give the size of TS-3, but would not yet yield a table-top due to the additional size of the two separate electrodes chambers of PROTO-SPHERA The costs would remain almost unaffected (�0.8), but the space available inside the vacuum vessel would be reduced, making difficult to allocate all the required components A reduction by 2.5 would yield a table-top experiment, but smaller than TS-3 It could reduce the costs (�0.5)at the price of: • Reducing��Formation~65 �s, <Te>=65 eV and �E

LG~80 �s at <ne>=1.8•1019 m-3 • Design and construction of a miniature project would be pointlessly challenging • The power supply would be complicated, dealing with formation times of about 50 �s


• Difficult controls and limited diagnostics for a physics of reduced purposes

REACTOR EXTRAPOLATION

24

With the same ratio Ip/Ie~Ip/Itf~1 Resistivity of a plasma centerpost > resistivity of a copper centerpost

unless a plasma temperature TPinch~700 eV is achieved If in PROTO-SPHERA Ip/Ie~4 is achieved Resistivity of a plasma centerpost > resistivity of a copper centerpost with Ip/Itf~1

unless a plasma temperature TPinch~300 eV is achieved In either case the impossibility of achieving in a screw pinch (of limited length) a temperature of many-100-eV hampers a direct reactor extrapolation of PROTO-SPHERA


On the base of the present knowledge one has better to consider as reactor-oriented a configuration in which the plasma is initiated by electrodes, like in PROTO-SPHERA, but is then sustained in absence of electrodes

CKF CONFIGURATIONS

25

A simply connected magnetic confinement scheme is obtained superposing two axisymmetric homogeneous force-free fields, both having

�

��

��

��

B =�B , with the same relaxation parameter �=�

��

��

0��

��

j •�

��

B /B2=14.066... in unitary sphere Chandrasekhar-Kendall Force-free fields Furth square-toroids

Coincidence of zero of and of fixes � =x1,4��/2x1,3=2.026...,


so that at R=0, Z=x1,3/x1,4=0.775... the zeroes coincide

CKF CONFIGURATIONS

26

The superposition of the two force-free fields is: � r�� =��1CK +� ��

F For �≥0.402..., in a simply connected region, toroidal current density j� has the same sign:

Chandrasekhar-Kendall-Furth force-free field (CKF)


CKF CONFIGURATIONS

27

CKF force-free-fields (�p=0) contain a magnetic separatrix with ordinary X-points (B≠0) A main spherical torus (ST), 2 secondary tori (SC) and a surrounding discharge (P)


Two degenerate X-points (B=0) are present (top/bottom) on the symmetry axis

CKF CONFIGURATIONS

28

Unrelaxed (�p≠0) CKF, calculated imposing �=�0j•B/B2=constant at the plasma edge If surrounding discharge is sustained, magnetic helicity is injected into the ST (reconnections at X-points), flowing down �<�>: �p concentrated in the same region


CKF CONFIGURATIONS

29

CKF, with this kind of <�> and p profiles, are stable in free boundary to ideal MHD perturbations with low toroidal mode numbers (n=1, 2, 3), at ST=2�0<p>ST/<B2>ST≈1/3


Trend of MHD stability with IST/Ie: same as in PROTO-SPHERA

CKF CONFIGURATIONS

30

and even in free boundary up to ST=2�0<p>ST/<B2>ST ≈1

Trend of MHD stability with �: same as in PROTO-SPHERA

IMPORTANCE of high � for a reactor: reduces cost and size Pfusion~�2B4 therefore higher ��lower B


nT�E~�/� {a2B2} therefore higher �� lower a at same ��

CKF CONFIGURATIONS 31

�ST=1, ratio IST/Ie=3, stable oscillations:

n=1 on P n=2 on ST n=2 on SC


Equatorial profiles: p(R), �(R) & j�(R) at �ST=1, IST/Ie=3

CKF CONFIGURATIONS

32

Method for injecting plasma current (or torque) in an unrelaxed CKF ?

Could CKF fusion reactors with �≈1, self-sustain their plasma magnetic field? Nonaxisymmetric resistive instabilities ��Unimpeded outflow from ST of part of the charged fusion products, via the magnetic separatrix, to the degenerate X-points (B=0)

Different orbits of co/counter-circulating fusion products on inboard/outboard of surrounding discharge, should drive (sufficient?) current and torque


This bootstrap-current-like effect could inject (sufficient?) helicity into the burning ST

CKF CONFIGURATIONS

33

Comparison of D-T burners (limited by 5 MW/m2 neutron wall loading) RHST ST

[m] IST , Ie [MA]

<TST>,TP[keV]

<ne> [1020m-3]

Bem

[T] �� P neutrons, Pcharged

[MW] 2 1.09 17.5, 2.7 12, 2.6 4.6 2.4 0.99 468, 117

1 1.54 35, 5.3 11, 2.6 4.4 3.4 0.43 1044, 261

Electrode breakdown of the plasma: screw pinch, then inductive formation of CKF


The current density to be injected by electrodes in order to start-up a D-T burner, before the inductive formation of the ST, is just the one of PROTO-SPHERA(je=0.8 MA/m2)

CKF CONFIGURATIONS

34

PROTO-SPHERA can be viewed as an unrelaxed CKF configuration where: • force-free screw pinch, fed by electrodes, replaces in part the surrounding discharge • "divertor" poloidal field coils replace the secondary tori

With limited modifications of the load assembly, PROTO-SPHERA could try the inductive formation of an unrelaxed (CKF) configuration


CONCLUSIONS

35

PROTO-SPHERA project is in the framework of Compact Tori (ST, Spheromak, FRC): Its particular goal is to form and to sustain a Flux-Core-Spheromak with a new technique and to show that DC helicity injection can sustain it on the resistive time-scale • Will advance the knowledge of DC helicity injection The magnetic configuration of the experiment has been designed aiming at a safety factor profile that is similar to the ones obtained in spherical tori with metal centerpost • Will complement the ST experiments (START, MAST, NSTX,…) The current density and power load on the electrodes (W) will advance the state of technology • Will be relevant to the design of divertors for the main tokamak line The major points that have to be demonstrated on PROTO-SPHERA are: • That the formation scheme is effective and reliable • That the configuration can be sustained in 'steady-state' by DC helicity injection • That the energy confinement is not worse than the one measured on spherical tori If these objectives are met, PROTO-SPHERA could try the inductive formation of a CKF • PROTO-SPHERA could lead to a proof-of-principle CKF experiment


PARAMETERS OF PROTO-SPHERA

36

Parameters of the spherical torus (ST): Equatorial, major, minor radius of the ST Rsph = 0.36 m , R = 0.20 m, a = 0.16 m Aspect ratio of the ST (R/a), Elongation A = 1.25, �� = 2.17 Toroidal ST plasma current Ip = 180 kA Safety factor of the ST at the edge q95 = 2.6 ST volume averaged electron density <ne>= 0.5•1020 m-3 ST volume averaged electron temperature <Te>= 140 eV Energy confinement time of the ST �E = 1.6 ms Resistive & Alfvén time of the ST �R = 70 ms, �A= 0.5 �s Magnetic Lundquist number of the ST S = 1.2•105 Total beta & poloidal beta of the ST �T = 10÷30%, �pol ≤ 0.15 Parameters of the screw pinch (SP): Equatorial radius of the SP �Pinch(0) = 0.04 m Longitudinal current in the SP Ie = 60 kA ...corresponding to a toroidal field BT0 = 0.05 T at R = 0.23 m ... ... including paramagnetism BT = 0.14 T at R = 0.23 m SP electron density ne

Pinch = 0.15•1020 m-3


SP electron temperature TePinch = 36 eV

Documents

The most investigated magnetic fusion configurations … Euratom-ENEA sulla Fusione PROTO-SPHERA Workshop, Frascati, 18-19/3/2002 C. Alessandrini, F. Alladio, G. Apruzzese, G. Bracco,