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Stellarators Jan Mlynář, Institute of Plasma Physics AS CR, v. v. i. PPST European Summer School, Prague 20th August 2009 What shall you learn in this talk? • reminder – why mg. field must be helical • definition of stellarators, their advantages • classical stellarator • torsatron • heliac • advanced stellarator • transport in stellarators • magnetic flux surfaces in stellarators • other alternatives of mg. field configuration besides tokamaks and stellarators, for example - reversed field pinch - levitated dipole - spheromac - magnetic mirror - linear pinches Field helicity In fusion facilities with closed configuration magnetic field must be helical in order to compensate gradB and curvature drifts, which have opposite direction for electrons and ions. z ∇ B R B Without helicity, any toroidal plasma would get polarised, which would result in immediate loss of stability due to ExB drift. Reminder: Tokamaks In a tokamak, field helicity is due to electrical current induced in its plasma. In a stellarator, by definition, magnetic field is configured by external coils only (no electrical currents in plasma). Pros and cons of a stellarator Advantage: no electrical current in the plasma means Æ no need to induce the current, i.e. stellarator is inherently suitable for a continous operation Æ no electrical current = no current instabilities (kinks) Æ field configuration almost independent of plasma Price to pay: No internal currents Æ From the Ampere’s law, ∇×=B 0()0 ⇒Brrdθ = ∫ θ with this constraint, stellarator can not be axially symmetric, stellarator plasmas must have complicated 3D shape Due to this, stellarators are much more complex to build, to understand kink instabilities and also suffer higher particle losses Very first stellarators – shape of number 8 Lyman Spitzer from Princeton, USA - the man behind first stellarators „Racetrack idea“ – a particle that moves along a magnetic field line regularly changes gradient B and curvature sign. But then, another idea came to mind – plasma could be twisted poloidally rather than toroidally. “Classical stellarator” In the classical stellarator, the vacuum vessel has toroidal shape (in blue) and toroidal field coils (in red), while additional helical coils (in green) impose the field helicity on plasma (in yellow). C- stellarator (later to become ST tokamak...) Helical coils in the classical stellarator Notice: In the classical stellarator, the helical coils must act in pairs with opposite direction of electric current (i.e. in dipoles). l ..... number of the dipoles n ..... periodicity of the dipoles in the toroidal direction Notice that it is not trivial to determine the magnetic field helicity in this configuration. Field helicity is NOT identical to the helicity of the dipoles !! l = 2, n = 5 stellarator (W2, W7-A) Classical stellarators W2 in the Deutsches Museum W1 WEGA (Greifswald) Wendelstein (Bayern, Germany) Field helicity in the classical stellarator Ihel.coil l = 3 l = 2 magnetic flux surfaces l = 1 l = 2 l = 3 a flux surface in 3D ( l = 2 ) the thick line shows a magnetic field line toroidal direction Field helicity in the classical stellarator Toroidal field coils Helical coils (parts closer to us) Electric current average field helicity Combining fields of the coils Mg. field line (illustrative, in 4 steps) Torsatron (“heliotron” in Japan) Torsatron is a modification to the classical stellarator, based on the idea “let us generate also the toroidal field by helical coils” Æ torsatron has helical coils only, with identical direction of current. “Basic torsatron” needs vertical field “Ultimate torsatron” replaces vertical field by varying pinch of the helical coils Torsatron (“heliotron” in Japan) CHS, Toki, Japan Coils of ATF, ORNL (RIP) Uragan, Kharkov Ukraine CAT, Auburn Univ., USA TJ-K, Karlsruhe .... and Large Helical Device (LHD), NIFS, Toki, Japan http://www.lhd.nifs.ac.jp/en/lhd/movie.html Heliac Another idea based on the classical stellarator: Instead of the helical winding around plasma, have helical plasma around a winding. Heliac H-1, Canberra, Australia TJ-II, CIEMAT, Madrid, Spain Advanced stellarator Yet another idea based on the classical stellarator: Let us combine toroidal field coils and helical coils into one set of “modular coils” Disadvantages: The resulting coils have complex geometry. Advantages: More compact. !! Further shaping of the coils is possible Æ mg. field optimisation !! Advanced stellarators UST-1 (built in a garage, Spain) W-7AS, IPP Germany (RIP) HSX, Univ Wisconsin, USA Advanced stellarators – NCSX ...RIP PPPL Princeton USA Wendelstein 7-X l = 2, n = 5 advanced stellarator with superconductive coils under construction in IPP Greifswald Wendelstein 7-X Field helicity in stellarators While in tokamaks the pitch of the field line decreases with distance from the plasma core, in torsatrons it increases and in other stellarators it is virtually constant. Neoclassical transport in the stellarators Due to the variations of the field along magnetic field lines, more particles are trapped in local magnetic mirrors (in field ripple) Trapped particles are lost due to drifts Æ neoclassical transport in stellarators must be higher than in tokamaks. Trapped particles dark – low mg.field light – high mg. field The helically trapped particles have serious consequences to neoclassical transport in particular in low collisionality plasma (ie low density or very high temperature) Magnetic lux surfaces in a stellarator • flux surfaces are produced by external field only, that is, they exist even in vacuum • advantage: they are pre-defined and modified independent of plasma parameters • advantage: unlike in tokamaks, flux surfaces can be experimentally studied using electron gun in vacuum • existence of the flux surfaces can be proved only for straight stellarator Magnetic flux surfaces in a stellarators • keep in mind, stellarator is not axially symmetric – unlike in tokamaks, shape of mg. Flux surfaces periodically changes in stellarators (with period n) • quality of flux surfaces can be improved by 3D optimisation and by selection of the helicity interval Optimisation of the advanced stellarators E.g. The W-7X stellarator has been optimised to achieve • weak islands • low Shafranov shift • low 1/ν transport • stable against ballooning • alpha-particle confinement • low bootstrap • technically feasible coils Best achieved values on stellarators LHD and W7AS Other alternatives to the stellarators reactor-relevant configuration • Reversed field pinches • (levitated) dipoles Closed (toroidal) and multipoles configurations • Spheromacs • ... • Magnetic mirrors Open (linear) • z- and θ- pinches configurations • ... • electrostatic confinement (fusor...) Reversed field pinch The effect of field reversal (the fact that the own field of plasma can reverse the direction of external toroidal field) was discovered at the ZETA toroidal z-pinch. ZETA (Harwell, UK) was the largest fusion experiment in 1950s. Its configuration is similar to tokamaks but with much weaker toroidal field. Field reversal – which stabilises plasma – was understood much later and is due to helicity conservation during pinch. Reversed field pinch - history ETA- BETA ZETA Field helicity and MHD modes in RFP Field reversal Notice safety factor is inversely proportional to the field helicity i.e. RFP helicity is reminiscent of torsatrons and „it is similar to tokamaks if you swap poloidal for toroidal and vice-versa“ Reversed field pinches in Europe EXTRAP-T2R, KTH, Sweden RFX, Padova, Italy major MHD feedback system installed Self-organised equilibrium View into the RFX chamber New, advanced mode of operation Single-helicity mode i.e. one strong MHD mode e.g. n = 8 observed - no magnetic chaos - no toroidally localised deformations Notice: RFP is axisymmetric but its plasma is not The pros and cons of RFP Advantages: • high beta (in theory up to 50%) Æ ohmic heating can go to substantially higher temperatures, possibly to ignition i.e. little or no additional heating required • low toroidal field is sufficient Æ no real need for superconducting coils, low forces MST – Madison, USA Disadvantages: • low q Æ lots of MHD instabilities causing chaotic paths of the magnetic field lines Æ poor confinement (10x worse than tokamaks) single null is a good hope • ohmic heating only Æ need for current drive • requires many fast feedback coils, hard to design for a fusion reactor TPE-RX, Tsukuba, Japan • continuous operation is very remote Spheromacs SSX, Swarthmore, USA Like tokamaks, but without central column Elegant, but it is difficult to get the shape and helicity! Several were operated, usually small. A bit bigger one “Proto-sphera” is under Proto-sphera, construction in Italy Frascati, Italy Internal ring devices Multipoles (minimum B) Dipoles (levitrons) Levitated octupole Levitated dipole LDX, MIT cross-section: In San Diego, http://psfcwww2.psfc.mit.edu/ldx/ the octupole Floating dipole magnet first proved the bootstrap current. Unique devices for fundamental research due to independent control of fields. Linear confinement (mirrors) A simple mirror has to be improved: 1. To achieve average min B (avoid interchange instability) Æ MHD anchors (baseball, yin-yang or cusps) baseball yin-yang CUSP 2. To minimise end losses (avoid kinetic instabilities) Æ thermal plugs Tandem mirrors GAMMA10 (1980s, Japan) density 5.1018 m-3, temperature10 keV confinement time 8 ms discharge duration 50 ms GOL-3 multimirror device BINP Novosibirsk, Russia Pinches: Fusion pioneers z-pinch θ-pinch Sausage instability More
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