Comments
Description
Transcript
riserva
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 ( jB =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 yexponent 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 ByT 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 m1 + g yml 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