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Home , Huemul Project, ZETA (fusion reactor)

Stellarators and linear devices

Gábor Veres/Gergő Pokol

BME NTI

Fusion devices 24. February 2020 Ingredients of fusion

Confinement and Stability

2 Confinement (force-free equilibrium)

+ Stability („rigidity” against perturbations)

3 Linear devices I

4 The

In slowly varying magnetic fields the constant magnetic moment is constant.

푣0 If the initial parallel velocity of the 푣⊥ particle is too large, the particle escapes 푣∥ 5 Linear devices II

6 Linear devices III (Magneto-Optical Traps, MOT)

 anti-Helmholtz coils and  Ioffe-Pritchard trap

 twisted metal bars to achieve 3D trapping  The B, versus position

7 The Bennett- (Z-pinch) 1D (linear) equilibrium

The simplest equilibrium is the Bennett-pinch (Z-pinch)

Why it does not work?: Suffers from numerous, violent instabilities 8 The theta-pinch 1D (linear) equilibrium

This equilibrium is stable, but transient.

9 The screw-pinch 1D (linear) equilibrium

This equilibrium is stable, but end-losses are substantial

10 Linear devices summary

Problems: Loss cones at the ends Instabilities

Proposed solutions: - Tandem mirror (electrostatic boundary) - rotation - Multiple mirrors (diffusive losses) around the axis - ICRH at ends (empty loss cones) - Inverse curved - strong NBI heating (non-thermal population) regions - long device (~100 m)

11 2D (toroidal) equilibrium

Partcle drifts in electrical and inhomogeneous magnetic fields:

This leads to an outward drift gradB-drift

Rotational transform (= helical magnetic field) is necessary E ExB-drift

ion gradB-drift

12 Rotational transform (iota)

휗 휄 = lim 푛 푛→∞ 2휋푛

2휋 푞 = 휄

The safety factor for

13 ZETA Reactor (UK)

„Zero Energy Thermonuclear Assembly” – from 1957

14 Plasma balls: 3D equilibrium

No „self-confinement” in 3D!!!!

15 Some history (fake news I)

Ronald Richter and the (1951), Thermotron → a complete fiasco

16 Some history (fake news II)

17 The helical field is necessary, but not sufficient

Vertical field + strong toroidal field to supress instabilities

18 zoology

19 Stellarator history

Lyman Spitzer with his Model-A stellarator in 1958 20 Stellarator history - Princeton

Model-B stellarator

T 1 2n D ~  B2

1 kT D  B 16 eB 21 Wendelstein

Wendelstein I-A (1961): „Racetrack” geometry Major radius: 35 cm Minor radius: 2 cm Magnetic field: 1 T Ohmic heating l=3 winding

Wendelstein I-B l=2 winding22 Classical stellarator

23 Wendelstein stellarators

Wendelstein II-A (1968): Torus geometry Major radius: 50 cm Minor radius: 5 cm Magnetic field: 0,6 T RF heating

24 Classical stellarator – WII-A

25 Wendelstein stellarators

Wendelstein II-B (1971): Torus geometry Major radius: 50 cm Minor radius: 5 cm Magnetic field: 1,25 T RF heating OH

26 Confinement depends on iota

Let’s design the iota-profile!

= 1/q

Ratios of small rational numbers are infavourable, because field line close on themselvs after a few turns

27 Modular stellarator

28 (Advanced) Wendelstein stellarators

Wendelstein 7-A (1976): Torus geometry Major radius: 2 m Minor radius: 0,1 m Magnetic field: 3,4 T Hydrogen plasma Neutral beam heating

29 Wendelstein stellarators

Wendelstein 7-AS (1988): Modular stellarator (5 modules) Partially optimized Major radius: 2 m Minor radius: 0,18 m Magnetic field: 2,5 T Hydrogen and plasma 30 W7-AS

31 Wendelstein stellarators

WEGA (1970 2001 2013): Torus geometry Major radius: 0,72 m Minor radius: 0,11 m Magnetic field: 0,9 T Hydrogen plasma Educational purpose

From 2014: Hybrid Illinois Device for Research and Applications

32 Magnetic geometry

33 Island divertor

34 W-7x stellarator (full 3D)

35 Wendelstein stellarators

1970 1980 1990 2000 2010

W7-X Greifswald Wega Garching München Wendelstein 7-AS

W 7-A

W 2-B

W 2-A

W1-B Wendelstein line stellarators W 1-A

36 Modular stellarator – HSX

37 Heliotron

38 Heliotron – LHD

39 Heliotron – LHD

40 Torsatron

41 Torsatron – TJ-K

42 Heliac

43 Heliac – TJ-II

44 Heliac – TJ-II

45 Stellarator magnetic fields

46 Sources

1. J.L. Johnson: The evolution of stellarator theory st Princeton, PPPl-3629 (2001) 2. H. Wobig et al.: Stellarator research at the IPP Garching, IPP report (2002) 3. M. Hirsch et al.: Major results form the stellarator Wendelstein 7-AS, Plasma Physics and Controlled Fusion, 50, 053001 (2008) 4. B.A. Carreras et al.: Progress in strellarator/heliotron research:1981-1986, , 28, 1613 (1988) 5. http://npre.illinois.edu/news/hidra%E2%80%99s-many-uses 6. http://www.hsx.wisc.edu/ 7. http://www.lhd.nifs.ac.jp/en/lhd/ 8. http://www.igvp.uni-stuttgart.de/forschung/projekte-pd/tjk.en.html 9. http://fusionsites.ciemat.es/tj-ii-2/ 10.Stellarator News: http://web.ornl.gov/sci/fed/stelnews/

47