Confinement of pure electron plasmas in the CNT stellarator

Columbia University In the City of New York

Thomas Sunn Pedersen

CNT

•  Background/introductory remarks –  CNT’s magnetic topology (a stellarator) –  Why study non-neutral plasmas in a stellarator? –  Basics of CNT operation: How we create pure electron plasmas,

how we diagnose them, and typical plasma parameters

•  Confinement studies in CNT –  Neoclassical predictions/expectations –  Transport studies:

•  Transport is driven by rods and neutrals •  Rod driven transport is understood •  Neutral driven transport indicates unconfined orbits

–  Numerical investigation of single particle orbits in CNT –  Recent experimental results: Improved confinement

•  Conclusion

Overview

Stellarator magnetic surface (field lines next slide)

CNT’s magnetic topology: A stellarator

CNT’s magnetic topology

CNT’s magnetic topology

The nested magnetic surfaces of the Columbia

Non-neutral Torus

1 Gourdon et al., Plas. Phys. Contrl. Nucl. Fus. Research p. 849 (1969) 2 Pedersen et al., Fusion Sci. Tech. 46 p 200 (2004)

CNT is the simplest stellarator ever built

CNT: First plasma Nov 2004

Electron beam at 200 eV, background gas is air at ~2*10-5 Torr

Leaking in a bit of air allows 3-D surface visualizations

•  There are unique properties relative to pure electron plasmas in other magnetic field configurations

•  Equilibrium is a minimum energy state (contrary to Penning and pure toroidal field traps) as a result of the stellarator topology

•  Stability properties are different

•  We can confine and study plasmas at any degree of neutralization all the way from pure electron to quasineutral

•  We may be able to create, confine, and study electron-positron plasmas

•  The transport properties of these plasmas are of interest to the fusion community –  Neoclassical transport in the regime of ‘extreme’ electric fields

a Pedersen and Boozer, PRL 88, 205002 (2002) b Boozer, Phys. Plasmas 11, p. 4709 (2004) c Lefrancois et al, Phys. Plasmas 12, p. (2005) d Pedersen et al., J. Phys. B 36, p. 1039 (2003)

Why study non-neutral plasmas in a stellarator?

Electron source: Thermionic emission from heated tungsten filament

Parallel transport fills field line on axis in ~ 1 µs

Perpendicular transport fills the rest of the surfaces

Reach steady state between emission and radial losses

Confinement time is electron inventory divided by emission (injection) current

How does one fill the volume of the stellarator with low temperature electron plasma?

Creation of pure electron plasmas

• Temperature: 2-7 eV in central region

• Density: ~1012 m-3

• Debye length ~ 1.5 cm

• Satisfies plasma criterion: CNT minor radius is ~15 cm

• Ion density <1% of electron density at base pressure

• Essentially pure electron plasma

• 2006: Confinement times up to 20 msec

• Stable equilibria - otherwise confinement would be <<1 msec

• Confinement still much lower than theoretical predictions

• This talk: Understanding of transport much improved - and so is the confinement time!

Typical plasma parameters

J. P. Kremer et al., Phys Rev Letters 97 095003 (2006)

• Fusion stellarator plasmas develop a (modest) net negative charge and a resulting negative potential if ions are poorly confined magnetically (“ion root”).

• This ambipolar potential gives |eφ/T| ~ 1, whereas in CNT’s pure electron plasmas, it’s |eφ/T|~10-50

• This leads to modest improvements in confinement (for both species) in fusion plasmas and should lead to significant confinement improvement for CNT

• This is essentially because the ExB drift dominates over grad B and curvature drifts (similar to LNT confinement)

Stellarator neoclassical transport can be studied in CNT

T. Sunn Pedersen and A. H. Boozer, Phys Rev Letters 88 205002 (2002)

€

vExBv∇B

≈∇φ /B

(Te∇B /eB2)≈eφTe

≈~ 10 - 50, CNT

~ 1, QNP (fusion stel.)

C N T

Particle confinement in a classical stellarator can be poor

Passing particles are confined - but it takes only one collision to turn a passing particle into a trapped particle

€

τ p ≈ τC ~ 10−2 sec

€

τDrift ≈ a /v∇B ~ 10−5 sec

Without an electric field: Magnetically trapped particles, a sizable fraction, drift out very quickly:

C N T

Orbits are closed due to ExB drift With strong E-field: Poloidal ExB closes orbits of magnetically trapped particles

C N T

Confinement should be enhanced due to ExB drift With strong E-field: Poloidal ExB closes orbits of magnetically trapped particles - small deviations

Assuming that the diffusive (density gradient driven random walk) transport dominates, one expects1 that τp~τc(a/λD)4 τc ~ 10 msec (10-8 Torr) A typical value of (a/ λD) is 10 So τp could be 100 seconds !

However, random walk diffusion is not the dominant collisional transport process when the electric field is strong. The electric field directly causes convective transport2 which scales as

τp~τc(a/λD)2 ie about 1 second confinement should be seen

1 Pedersen and Boozer, PRL (2002)

2. Berkery and Boozer, Phys. Plasmas (2007)

C N T

Experimental measurements of confinement and transport

• Two rods gives twice as much transport as one rod

• The rods are insulating, so they are not steady state sinks for electrons

• They are large electrostatic perturbations - drives ExB transport

Insulated rods drive transport

J. P. Kremer et al., Phys Rev Letters 97 095003 (2006)

Insulated rods charge up negative relative to plasma to self-shield Resulting ExB drift pattern convects particles along the rod all the way to the open field lines

We made a quantitative model of the rod induced ExB transport, including Debye shielding of the negatively charged rod. Very close to the rod, the transport is low (no density) and far away, it’s also low (Debye screened E-field)

Insulated rods limit confinement

J. W. Berkery et al., Phys. Plasmas 14 062503 (2007)

Good quantitative and excellent qualitative agreement between experiment and rod model

Comparison to experimental data

J. W. Berkery et al., Phys. Plasmas 14 062503 (2007)

Voltage dependence

1/B dependence

Neutrals also degrade confinement

Rod driven and neutral driven transport is separated

Neutral collision driven transport

The neutral driven transport is much greater than anticipated

We lose an electron after ~ 1 electron-neutral collisions

This transport has a component that is independent of B and a component that scales as B-1.5 - the second scaling has been observed in other non-neutral experiments1,2 and may be linked to trapped particle losses. The B-field independent losses are also consistent with bad orbits

1. Stoneking et al 2. Kabantsev et al.

Numerical analysis of electron orbits in CNT

•  Given these experimental findings, we should investigate the particle orbits in CNT in much more detail

•  CNT student Benoit Durand de Gevigney has developed a code that calculates the particle orbits in CNT

1: No electric field (single particle - no space charge) Magnetically trapped particles expected to drift out - CNT is not optimized

Single particle orbit movie:

1: No electric field (single particle - no space charge) Magnetically trapped particles expected to drift out - CNT is not optimized

Statistics: Start 1000 4 eV particles out and follow them

2: Strong electrostatic potential conforming to flux surfaces

Expectation: Excellent orbits, forced to rotate poloidally by ExB

Movie of single particle orbit

2: Strong electrostatic potential conforming to flux surfaces

Expectation: Excellent orbits, forced to rotate poloidally by ExB

3: Electrostatic potential varying on magnetic surfaces Until fall 2007, and for all the experiments discussed so far, the internal coil vacuum “jackets” and the vacuum chamber were the electrostatic boundary condition for our plasmas (grounded).

We model this complicated boundary condition (crudely) in our 3D equilibrium code. This gives us the full 3D electrostatic potential - showing rather large variation on a magnetic surface. That is input into orbit follower.

3: Electrostatic potential varying on magnetic surfaces

3: Electrostatic potential varying on magnetic surfaces Is there a substantial fraction of such unconfined orbits?

Yes, this is a big problem on the outer surfaces (small problem on the innner surfaces)

Intuitive picture of collisionless loss orbits with E •  ExB (perpendicular motion) carries the electron along the

electrostatic potential contour

•  The parallel motion of passing electrons (combined with rotational transform) carries the electrons along the magnetic surface, moving them poloidally

•  By switching between potential contours and magnetic surfaces, particles can make enormous radial excursions

See Benoit Durand de Gevigney’s poster for more transport modeling results - including comparisons with experimental results

Flux surface conforming electrostatic boundary

•  With a flux surface conforming electrostatic boundary condition, we expect to see significantly improved confinement

•  Installed summer 2007

•  Proper alignment with magnetic surfaces was a slow process

•  13 individual copper sections

•  Can be used as a capacitive probe too (work in progress)

•  Meshes can be biased individually to perturb the plasma

Results with new mesh installed 190 ms

See Paul Brenners poster for more on these experimental confinement results

Order of magnitude improvement!

Rod driven transport is significantly lower now (factor of 6)

We also increased our maximum operating B-field to 0.15 T from 0.1 T

What about the neutral driven transport? (We expected that to be improved)

Results with new mesh installed

The picture is not yet clear regarding neutral collisions. A preliminary conclusion: The neutral driven transport is strongly reduced but primarily due to reduction in the neutral pressure (neutral collision frequency). It looks like electrons are still lost after order unity collisions.

See Brenner’s poster for more results.

190 ms

Transport Jumps

When operating with conditions that increase radial transport significantly (low B, high bias voltage, high neutral pressure, several rods) we observe abrupt transport jumps

These can be as large as a factor of 2 They decrease confinement time by about that much See Michael Hahn’s and Paul Brenner’s posters for more on these observations

Electron-positron plasmas in CNT? Unique and relatively simple plasma physics due to perfect mass symmetry:

•  No ion acoustic waves

•  Other wave types collapse into just a couple of waves

•  “The hydrogen atom of plasma physics”

•  Have not been created yet on Earth

How?

Inject positrons into an initially pure electron plasma, neutralizing it

•  First, create a pure electron plasma ‘target’:

•  Cold (small Debye length)

•  Well confined

•  No internal material objects

•  Plasma stays around after injection and retraction

•  Develop instantaneous source of ~1012 of cold positrons (C. Surko, J. Danielson et al., UCSD, work in progress)

•  Develop injection method with >10% efficiency (we have ideas)

•  Non-neutral plasmas on magnetic surfaces:

•  Unique physics

•  Largely unexplored territory

•  Radial transport: Driven by rods, and neutrals

•  Rod transport well understood

•  Evidence of poor orbits

•  Confinement has been improved to 190 msec (previous record: 20 msec) •  Mostly due to reduction in rod driven transport, strangely

•  We still have plenty of mysteries

•  Electron-positron plasmas: We are making progress

Summary

Acknowledgements CNT group

John W. Berkery

Allen Boozer

Quinn Marksteiner

Michael Hahn

Benoit Durand de Gevigney

Paul Brenner

Xabier Sarasola Martin

Remi Lefrancois

Jason Kremer

More CNT results: Upcoming talk and poster session

PPPL (CNT design support)

Neil Pomphrey

Wayne Reiersen

Fred Dahlgren

CNT undergraduates Naveed Ahmad

Sarah Angelini

Charles Biddle-Snead

Dennis Boyle

Joanna Corby

Paul Ennever

Avi Grumet

Stacey Hirsh

Elliot Kaplan

Mark Kendall

Josh Narciso

Mike Shulman

Katherine Velas

(and more) Kyoto Inst. Tech.

Haru Himura