Associazione Euratom-ENEA sulla Fusione -----
11
RISERVA
Culham 15-17 September 2003
Associazione Euratom-ENEA sulla Fusione -----
ProtoSphera Parameters
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, k
= 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
tE
= 1.6 ms
Resistive & Alfvén time of the ST
tR
= 70 ms, tA= 0.5 ms
Magnetic Lundquist number of the ST
S
= 1.2•105
Total beta & poloidal beta of the ST
bT
= 10÷30%, bpol ≤ 0.15
Parameters of the screw pinch (SP):
Equatorial radius of the SP
rPinch(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
nePinch = 0.15•1020 m-3
SP electron temperature
TePinch = 36 eV
Culham 15-17 September 2003
Associazione Euratom-ENEA sulla Fusione -----
Why ULART ?
Magnetic line of
forces
Conventional Tokamak
Spherical Torus
High
Field line in Bad
Curvature region
Low
High
Geodesic
Curvature
Low
High
Neoclassical
transport
Low
High
Micro-instability
related to trapped
particles
Low
Culham 15-17 September 2003
Associazione Euratom-ENEA sulla Fusione -----
Spheromaks
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 very high filling pressures and kV voltages
Big amount of neutrals and impurities are released from the gun
The Spheromak formated 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 low voltages (~100 V) and will not undergo any expansion
Culham 15-17 September 2003
Associazione Euratom-ENEA sulla Fusione -----
Flux-Core-Spheromak obtained on the TS-3
Filling gas (pH~2•10-2 mbar); break-down (Ve~1 kV) using two plasma guns
Screw pinch current increases: toroidal plasma, non-linear kink: qPinch<1÷2
Compression coils pulsed: flux swing drive much of toroidal plasma current
After formation (~60 ms), the configuration was sustained for 20 msec, i.e. 30•tA
PROTO-SPHERA aims at sustaining the toroidal plasma through DC helicity
injection
Culham 15-17 September 2003
Associazione Euratom-ENEA sulla Fusione -----
Some ULART Features
Higher MHD stability and high average
total beta values: bT=2m0<p>Vol/BT2
(bT=40% with baxis=70% on START)
START : relatively high energy
confinement times and density limits with
H-mode in NBI X-point discharges
High bT
Culham 15-17 September 2003
Associazione Euratom-ENEA sulla Fusione -----
Helicity Injection
 The plasma with open field lines (intersecting
electrodes) has b~0, therefore ||
 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
Culham 15-17 September 2003
Associazione Euratom-ENEA sulla Fusione -----
mST & k
PROTO-SPHERA aims at a ST elongated k~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 mSTRsph≤4.2
Culham 15-17 September 2003
Associazione Euratom-ENEA sulla Fusione -----
ST, Spheromak, FRC
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
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 has
been soundly and fully demonstrated
Culham 15-17 September 2003
Associazione Euratom-ENEA sulla Fusione -----
Formation Time
TS-3 took 80 ms to reach Ip/Ie=1.2
Scaling up as S1/2tA (Sweet-Parker reconnection)
and including all passive currents:
t= t0-100ms
t= t0+300ms
t= t0+600ms
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
Culham 15-17 September 2003
Associazione Euratom-ENEA sulla Fusione -----
Stability
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 bST=2m0<p>ST/<B2>ST
With bST~30%
Ip can reach a value of 1•Ie
With bST~20%
Ip can reach a value of 2÷3•Ie
With bST~10%
Ip can reach a value of 4•Ie (design limit)
Culham 15-17 September 2003
Associazione Euratom-ENEA sulla Fusione -----
Reasons to push towards the
Ultra Low Aspect Ratio Torus (ULART, A ≤ 1.3)
 the critical central conductor cannot be shielded
it is bombarded by neutrons (cannot be a superconductor)
it should be periodically replaced
 But the ULART does not leave enough space for an ohmic
transformer and requires noninductive current drive
The bpol=2m0<p>Vol/Bpol2 marks
the distance from a force free-state
( jB =0).
 In an ST( Bpol ~ BT )
 A high bT (40%) plasma in an
ST is much nearer to a force-free
configuration than a low bT (4%)
plasma in a Tokamak
Culham 15-17 September 2003
Associazione Euratom-ENEA sulla Fusione -----
Conclusion
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
Culham 15-17 September 2003
Associazione Euratom-ENEA sulla Fusione -----
Image of PROTO-PINCH Hydrogen plasma with
Ie=600 A, B=1 kG.
PROTO-PINCH has produced
Hydrogen and Helium arcs in the
form of screw pinch discharges.
Pinch Length : 75 cm
Stabilizing Field : 1.5 kG
Safety Factor qPinch≥2
Ie = 670 A
Emax = 6.7 A/cm2
Vpinch = 80 –120 V
Vcathode = 14.5 V
Culham 15-17 September 2003
Associazione Euratom-ENEA sulla Fusione -----
Cathode Treats , Recipes & Results
Filling Pressure 1 10-3 – 1 10-2
AC current for heating the cathode, to spread the ion
plasma current over the filaments.
Time required for heating the cathode circa 15 s.
 Icath=550-590 A (rms.) at Vcath=14.5 V (rms.)
allows for Ie=600-670 A of plasma current Ie/Icath≈1.
 Pcath≈ 8.5 kW allows for Pe≈50-70 kW into the Pinch
 No damages after  400 shots at Ie= 600 A, Dt = 2-5 sec
Culham 15-17 September 2003
Associazione Euratom-ENEA sulla Fusione -----
Anode
a
b
 PWAnode = 2/3 (670 120) KW  56 KW ( module)
 Asurface= 1.8 10-3 m2
 Dpw = PW/ Asurface 30 MW/m2
 anode arc anchoring with Cathode DC heated (a)
 No Anode anchoring with AC cathode heating (b)
No Damages after
1000 discharges
Material: W 95% Cu5%.
Anode : Puffed Hollow
Culham 15-17 September 2003
Associazione
Euratom-ENEA
sulla----Fusione
Associazione
Euratom-ENEA
sulla Fusione
HeliConical Coil Test
Test Results :
Very Small
Displacement after 2700
Sec at 2700 C
PROTO-SPHERA Workshop
- Frascati,
18- 2003
Culham
15-17 September
Associazione Euratom-ENEA sulla Fusione -----
Cathode Layout
Material
Plates: Molybdenum
Columns:Tantalum
Insulator : Alumina
Coils : Pure W
Module Power = 8.4 KW
Module Current = 670 A
Module Voltage = 14.5 V
Wire Number = 4
Wire Length = 40.0 cm
Wire Surface = 4X25 cm2
Wire Temp = 2600 C
Wire Em = 6.7 Amp/cm2
Wire Weight = 4X22 Gr.
Culham 15-17 September 2003
Associazione Euratom-ENEA sulla Fusione -----
HeliConical Coil
 Null Field
 Optimize
Temperature
Distribution
 Optimize
Weight
Distibution
 Ie =167 A
(each coil)
Culham 15-17 September 2003
Associazione Euratom-ENEA sulla Fusione -----
Structural Analysis
Max
VonMisess
Stress 0.16
Kg/mm2
Max
Displacement
42.9 mm
 Coil Safety
Factor = 5.3
Culham 15-17 September 2003
Associazione Euratom-ENEA sulla Fusione -----
Emissivity vs Temperature (1)
Culham 15-17 September 2003
Associazione Euratom-ENEA sulla Fusione -----
Conclusion
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 'steadystate' 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-ofprinciple CKF experiment
Culham 15-17 September 2003
Associazione Euratom-ENEA sulla Fusione -----
H
Visible
Spectroscopy
H2 Zoom
2
Å
Å
Spectral lines of
filling gas (H2/He
) and impurities
Enlarged
1 eV < Te  3.0
eV - No HeII
(4686 Å)
He zoom
He
Å
He
Å
Very few
impurities
OII & CIII at a
count level  10-2
of the largest
Helium line
counts
Culham 15-17 September 2003
Associazione Euratom-ENEA sulla Fusione -----
Density Measurements
2mm microwave interferometer with 140 GHz oscillator :
B = 1.25 kG : ne = 1.4 1019 m-3 per fringe  ne ~ 6 1019
m-3
Ie
fringes
Density measurable
In Helium discharge up to
Ie = 200 A
Line-averaged electron
density increase linearly with
current Ie
Helium ionization degree
is about 16% at filling
pressure of 4 10-3 mbar & Ie=
200 A
Culham 15-17 September 2003
Associazione Euratom-ENEA sulla Fusione -----
MODELING of PROTO-PINCH PLASMA
 Spectroscopy  1<TePinch<3 eV
Ohmic input = electron flow convected flux  TePinch = 2
eV
Interferometry suggests  plasma 50% ionized at
Ie=600 A  pH2=8•10-3 mbar gives: nePinch = 2•1020 m-3
However estimated Ohmic input PW= 4kW
 main loss in electrode plasma sheaths Pelectrodes= 46 kW
 power injected near the electrodes gives: Teelectrodes = 0.4
eV
 constant electron pressure gives: neelectrodes = 5•1020 m-3
Culham 15-17 September 2003
Associazione Euratom-ENEA sulla Fusione -----
EXTRAPOLATION to Screw Pinch of PROTO-SPHERA
Assuming same plasma near the electrodes at Ie=60 kA
Teelectrodes = 0.4 eV, neelectrodes = 5•1020 m-3
Power into electrode sheaths Pelectrodes= 100•46 kW = 4.6 MW
 In the main body of the discharge (far from electrode sheaths)
Ohmic input = electron flow convected flux:
TePinch = 36 eV  constant electron pressure:
nePinch = 1.5•1019 m-3
 Ohmic input PW = 5.4 MW
OHMIC
PW
5.4 MW +
SHEATHS
Pelectrodes
4.6 MW +
Helicity Injection
PHI
0.6 MW =
TOTAL POWER
PPinch
10.6 MW
Culham 15-17 September 2003
Associazione Euratom-ENEA sulla Fusione -----
1.
2)
3)
4)
5)
6)
7)
10
Panel Questions & Answers
Is the physics basis for undertaking an experiment as proposed with
PROTO-SPHERA adequate?
OK, BUT We recommend that a wider range of operation scenarios of m
and pressure profiles be analysed... (equilibria & stability &n0 stability )
Are the PROTO-PINCH electrode experiments a sufficient technical basis
for a reliable electrode operation in PROTO-SPHERA?
OK, BUT… are not yet adequate for reliable multi-electrode operation...
… In particular, is the proposed size adequate for the purposes of a
Concept Exploration Experiment? .. OK
How likely is .... to advance the present state of science and technology
substantially.. OK
.. likely to produce new information that is adequate as basis to
extrapolate to a SPHERA device that achieves fusion relevant
parameters? OK
What diagnostics should be planned in order to properly measure the
properties of the PROTO-SPHERA plasma? OK
What are the unique contributions of the proposed experiment to the
world magnetic fusion programs, and in particular to the European
Magnetic Fusion Program during the VIth FP? OK
Culham 15-17 September 2003
Associazione Euratom-ENEA sulla Fusione -----
11
Equilibria Computation Before Panel
p(y) = pe=constant
p(y) = pe + Cp(y-yX)1.1
2
dia
2
dia
I
I

y  I  y  yX 
1.1
2
y  I  CI y-yX 
2
e
2
e
for y<yX
for y≥yX
for y < yX
for y ≥ yX
inside the SP and
inside the ST
inside the SP and
inside the ST
Ie Screw Pinch longitudinal current, pe is the pressure inside the SP and
yX is the poloidal flux function at the separatrix the I2dia yexponent
in the SP is =2
Idia(y)y
Screw Pinch is force-free
relaxation parameter m=m0 j• B/B
.2
Constant inside Pinch
• For every Equilibrium calculation the poloidal beta of
the Spherical Torus is an input parameter as well as the
total toroidal current Ip inside the ST and Ie inside SP
Culham 15-17 September 2003
Associazione Euratom-ENEA sulla Fusione -----
12
Panel Questions Concerning Scenarios
..We recommend that a wider range of operation scenarios of m and pressure
profiles be analysed to engender greater confidence in the successful operation of
the machine before considering moving towards any construction phase.
Screw Pinch force-free (constant p(y) inside the SP) reasonable
( open magnetic field lines)
Hypothesis that m(y)=constant inside it could be questionable.
An investigation has been performed by varying 

2
2
i.e. the current inside the SP: Idia y   Ie  y  y X 
A wider range of scenarios explored inside ST varying h and e
dI
dF
yc=yX+h×(ymax-yX)
mdia  m0 dia  m0 CI
dF
dy
dF
dy
dy
dy
 ( y - yX ) 
Ie 

=
1 - e sin 

yX 
2( yc - yX ) 
I
= e 1 - e
yX
yX ≤y≤yc
y>yc
Culham 15-17 September 2003
Associazione Euratom-ENEA sulla Fusione -----
14
Stabilty
• In PROTO-SPHERA resistive MHD instabilities are
required to inject magnetic helicity from SP into ST
• The combined configuration must be MHD stable
Features of MHD stability codes (STABLE)
•Boozer coordinates on open field lines are joined to the
closed field lines Boozer coordinates at the ST-SP interface
•Boundary conditions at the ST-SP interface
•Vacuum magnetic energy in presence of multiple plasma
boundary
•2D finite element method for accounting the perturbed
vacuum energy
r
•Plasma on the symmetry axis require a well suited x
(perturbed displacement) decomposition, to avoid perturbated
potential energy divergence for R=0.
Culham 15-17 September 2003
Associazione Euratom-ENEA sulla Fusione -----
16
Stability: CASE n=0
• The perturbed displacement , has in STABLE code been
decomposed in terms of the normal xy, binormal hy and parallel m
components
• For n=0 the displacements x T   T y T e  and x B  ByT B
must be zero because, the flow along field lines and the
toroidal flow do not contribute to the perturbate plasma
potential magnetic energy but they contribute to the
perturbed kinetic energy, creating
r spurious eigenvectors
and eigenvalues. A modified x displacement
decomposition has been adopted to solve this problem
(new code:STABLEN0MU).
Culham 15-17 September 2003
Associazione Euratom-ENEA sulla Fusione -----
Year 1
TIME SCHEDULE
Year 2
Check
Assembly
ASSEMBLY
WORK
Tender
Orders
Work
Final
check
PUMP,GAS,
CONTROL
Tender
Orders
Assembly
Final
check
Design
Tender
Year 4
Construction
LOAD
ASSEMBLY
Contract
Year 3
PF COILS
Design
Contract
Tender
Construction
Check
ELECTRODE
Design
Contract
Tender
Construction
Check
POWER
SUPPLY
Design
Tender
Construction
Check
ELECTRICAL
WRK
Design
Tender
Work
Check
Assembly
Final
check
Guarantee
Final
check
Guarantee
Guarantee
Assembly
Check
Final
check
Assembly
Final
check
Guarantee
Final
check
Guarantee
Culham 15-17 September 2003
Associazione Euratom-ENEA sulla Fusione -----
Some Steps
•
•
Following a formal request by the Euratom-ENEA Steering
Committee in December 1999,
•
•
After the ENEA internal peer-review and CTS review system (March
2000-March 2001) assigned to the PROTO-SPHERA project the
mark 45/54,
•
•
The PROTO-SPHERA Workshop held on March 18-19, 2002
• Questions raised by panel
Culham 15-17 September 2003
Associazione Euratom-ENEA sulla Fusione -----
CKF
A simply connected magnetic confinement scheme is
obtained superposing two axisymmetric homogeneous
force-free fields, both having  B =m B , with the same
relaxation parameter m=m0•/B2=14.066... in unitary sphere
Chandrasekhar-Kendall
Force-free fields
Coincidence of zero of
and of
Z=x1,3/x1,4=0.775... the zeroes coincide
fixes
Furth square-toroids
l =x1,4 /2x1,3=2.026..., so that at R=0,
Culham 15-17 September 2003
Associazione Euratom-ENEA sulla Fusione -----
CKF
F
The superposition of the two force-free fields is: y r= y CK
m1 + g yml
For g≥0.402..., in a simply connected region, toroidal current
density j has the same sign:
Chandrasekhar-Kendall-Furth force-free field (CKF)
Culham 15-17 September 2003
Associazione Euratom-ENEA sulla Fusione -----
CKF
•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 Xpoints (B=0) are present
(top/bottom) on the
symmetry axis
Culham 15-17 September 2003
Associazione Euratom-ENEA sulla Fusione -----
CKF Stability
CKF, with this
kind of <m> and
p profiles, are
stable in free
boundary to
ideal MHD
perturbations
with low
toroidal mode
numbers (n=1,
2, 3), at b
ST=2m0<p>ST/<B
2> ≈1/3
ST
Trend of MHD stability
with IST/Ie:
same as in PROTO-SPHERA
Culham 15-17 September 2003
Associazione Euratom-ENEA sulla Fusione -----
CKF Stability
Even in free boundary up to b ST=2m0<p>ST/<B2>ST ≈1
Trend of MHD
stability with b:
same as in
PROTOSPHERA
IMPORTANCE of high b for a reactor: reduces cost and size
Pfusion~b2B4
therefore
higher b lower B
nTtE~b/c {a2B2}
therefore
higher b lower a at same c
Culham 15-17 September 2003