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Home , Fusor

Jan Mlynář, Institute of 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 , their advantages • classical • torsatron • heliac • advanced stellarator • transport in stellarators • magnetic flux surfaces in stellarators • other alternatives of mg. field configuration besides and stellarators, for example - - - spheromac - - linear pinches Field helicity

In fusion facilities with closed configuration must be helical in order to compensate gradB and curvature drifts, which have opposite direction for and .

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 , 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 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 (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

• advantage: unlike in tokamaks, flux surfaces can be experimentally studied using 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 (...) 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 stable, but (and kinks, remind) engineering difficulties Fusion pioneers and their comeback

Scylla in Los Alamos: the first to see

Z-facility in Sandia, USA z pinch in W as an option to ingite inertial fusion Plasma focus http://www.focusfusion.org/

Megajoule plasma focus in IPPLM Warsaw, Poland Final remarks • tokamaks have the best confinement and, as a consequence, they also won most of human efforts

• stellarators have no problems with continuous operation and are much safer against major instabilities

• reversed shear pinches work with higher density at a given mg. field Æ in principle do not need external heating

• other configurations seem suitable rather for basic plasma research (levitrons, spheromacs) or applications like sources (mirrors, pinches) ITER platform panorama