Confinement of pure electron plasmas in the CNT stellarator Thomas Sunn Pedersen CNT Columbia University In the City of New York
Overview • 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
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
CNT is the simplest stellarator ever built 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: First plasma Nov 2004
Leaking in a bit of air allows 3-D surface visualizations Electron beam at 200 eV, background gas is air at ~2*10 -5 Torr
Why study non-neutral plasmas in a stellarator? • 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)
Creation of pure electron plasmas Electron source: Thermionic emission from heated tungsten filament Parallel transport fills field How does one fill the line on axis in ~ 1 µ s volume of the Perpendicular transport stellarator with low fills the rest of the surfaces temperature electron Reach steady state plasma? between emission and radial losses Confinement time is electron inventory divided by emission (injection) current
Typical plasma parameters • Temperature: 2-7 eV in central region • Density: ~10 12 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! J. P. Kremer et al., Phys Rev Letters 97 095003 (2006)
Stellarator neoclassical transport can be studied in CNT • 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 |e φ /T| ~ 1, whereas in CNT’s pure electron plasmas, it’s |e φ /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) ~ 10 - 50, CNT v ExB ( T e ∇ B / eB 2 ) ≈ e φ ∇ φ / B ≈ ≈ v ∇ B T e ~ 1, QNP (fusion stel.) T. Sunn Pedersen and A. H. Boozer, Phys Rev Letters 88 205002 (2002)
Particle confinement in a classical stellarator can be poor Without an electric field: Magnetically trapped particles, a sizable fraction, drift out very quickly: τ Drift ≈ a / v ∇ B ~ 10 − 5 sec Passing particles are confined - but it takes only one collision to turn a passing particle into a trapped particle τ p ≈ τ C ~ 10 − 2 sec 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: Assuming that the diffusive (density Poloidal ExB closes gradient driven random walk) transport orbits of magnetically dominates, one expects 1 that τ p ~ τ c (a/ λ D ) 4 trapped particles - τ c ~ 10 msec (10 -8 Torr) small deviations A typical value of (a/ λ D ) is 10 So τ p 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 transport 2 which scales as τ p ~ τ c (a/ λ D ) 2 ie about 1 second confinement should be seen 1 Pedersen and Boozer, PRL (2002) C N T 2. Berkery and Boozer, Phys. Plasmas (2007)
Experimental measurements of confinement and transport C N T
Insulated rods drive 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 J. P. Kremer et al., Phys Rev Letters 97 095003 (2006)
Insulated rods limit confinement 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) J. W. Berkery et al., Phys. Plasmas 14 062503 (2007)
Comparison to experimental data 1/B dependence Voltage dependence Good quantitative and excellent qualitative agreement between experiment and rod model J. W. Berkery et al., Phys. Plasmas 14 062503 (2007)
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 experiments 1,2 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
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