Introduction to Stellarators and to the National Compact Stellarator
Experiment (NCSX)

Allan Reiman

National Compact Stellarator Experiment (NCSX) is in construction phase
at PPPL.

-   NCSX to be completed in 2009 at estimated cost \~ \$94 million.

Operating budget expected to be similar to that of NSTX.

-   When complete, NCSX will embody new type of stellarator
    configuration, combining desirable features of optimized
    stellarators and advanced tokamaks.

Six of the grad student seminars to be devoted to stellarators.

This Talk

-   Introduction to stellarators.

-   Physics configuration design of NCSX.

-   Issue of equilibrium flux surfaces.

> Invention of Stellarators Grounded in a Key Insight
>
> Early 1950's: Recognition that some desirable properties of magnetic
> fields are lost when symmetry is imposed.
>
> ![](media/image1.jpeg){width="1.9165354330708662in"
> height="1.9165354330708662in"}
>
> Particle accelerators: strong focusing. (Courant, Livingston, Snyder)
>
> Early implementation used magnetic quadrupoles in alternating
> directions.
>
> Transformed subsequent accelerator design.

![](media/image3.jpeg){width="2.141732283464567in"
height="2.5374015748031495in"}

-   Rotational Transform: Introduction

Purely toroidal field cannot confine plasma in torus:

![](media/image14.jpeg){width="5.8902777777777775in"
height="8.997916666666667in"}

A 3D Magnetic Field Can Produce Rotational Transform Even with *I*~t~ =
0

![](media/image3.jpeg){width="2.708267716535433in"
height="3.208267716535433in"}![](media/image15.jpeg){width="3.322834645669291in"
height="1.708267716535433in"}

Data indicates that scaling of confinement with rotational transform is
approximately the same, independent of whether ι generated by current or
3D field.

![](media/image16.wmf){width="6.1618055555555555in"
height="6.288888888888889in"}

![](media/image17.wmf)

Nonaxisymmetry Also Provides Additional Control over Properties of Field
that Affect Stability

-   Global shear: ι'.

-   Local shear: pitch of field line.

-   Magnetic well, dV/dΨ~t~, where V(Ψ~t~) is volume within flux surface
    containing toroidal flux Ψ~t~. (Also 2^nd^ order for small helical
    field.)

# In Practice, Stellarators Rarely Disrupt

-   Present day stellarator experiments do not disrupt in normal
    operation, even when pushing parameters.

    -   e.g. density limit gives slow loss of energy on transport time
        scale.

-   W7AS team has been able to induce disruptions in specially prepared
    scenarios (e.g. ramping through m/n = 2/1 rational surface in plasma
    with very low shear and current profile predicted to be tearing
    unstable.)

Introduction of Nonaxisymmetry Also Brings with it Some Difficulties

![](media/image18.png){width="3.8159722222222223in" height="4.46875in"}

-   Potential loss of flux surfaces

    -   Can generally remove resonant vacuum fields that break flux
        surfaces without affecting physics properties, but flux surfaces
        at finite beta remains an issue.

![](media/image19.jpeg){width="3.2333333333333334in"
height="2.7416666666666667in"}Introduction of Nonaxisymmetry Also Brings
with it Some Difficulties (continued)

-   Drift trajectories generally not well behaved.

    -   Can give large neoclassical transport at low collisionality.

    -   Confinement of energetic alpha's a particular issue.

-   Increased complexity of coils and support structure.

    -   Difficult to assess quantitative impact on reactor costs at this
        time.

    -   Will need to evaluate trade-offs relative to tokamak in terms of
        e.g.: feedback control systems for external kinks; current drive
        systems, including those required for neoclassical tearing mode
        stabilization.

    -   Some small degree of nonaxisymmetry will not greatly impact
        cost.

Contemporary stellarators rely on modern developments in theory and
computation to address these difficulties.

-   Transport:

    -   Classes of configurations identified for which
        three-dimensionality does not adversely impact transport. e.g.
        "quasi-symmetric" configurations. To be discussed in seminars by
        Harry Mynick.

    -   Contemporary stellarator design uses "optimization" codes to
        target good drift trajectories while also incorporating other
        desirable features.

-   Flux surfaces:

    -   Two codes developed to calculate equilibrium flux surfaces: PIES
        code (Princeton), HINT code (Japan).

    -   NCSX used PIES code to help guide design with good surfaces.

    -   Optimization procedure adopted by W7X verified to provide good
        surfaces. (Princeton-German collaboration on PIES calculations
        for W7X.)

        ![](media/image20.jpeg){width="9.559027777777779in"
        height="6.9375in"}

        ![](media/image21.jpeg){width="6.25in"
        height="7.411111111111111in"}

        ![](media/image22.jpeg){width="5.416666666666667in"
        height="7.2125in"}

NCSX design combines favorable features of advanced tokamaks with those
of drift-optimized stellarators.

**Design strategy:**

-   ![](media/image23.png){width="2.104330708661417in"
    height="3.3015748031496064in"}![](media/image24.png){width="1.5799212598425196in"
    height="2.8897637795275593in"}Use advanced tokamak equilibrium as
    starting point.

-   Use numerical optimizer to introduce 3D deformation to address
    tokamak problems while preserving desirable tokamak properties.

-   Key tokamak issues addressed:

    -   Reduce or eliminate need for rf current drive.

    -   Stabilize neoclassical tearing modes via rotational transform
        profile.

    -   Stabilize external kink modes and vertical instabilities via
        shaping.

PIES Calculations for NCSX: 1. Identification of Fixed Boundary
Equilibria with Intrinsically Good Flux Surfaces

![](media/image25.png){width="3.748425196850394in"
height="4.088188976377952in"}

PIES Calculations for NCSX: 2. Design of Coils to Preserve Flux Surfaces

An optimizer has been built around the PIES code to modify the coil
design to heal islands while preserving desired physics and engineering
properties.

![](media/image26.png){width="5.416535433070866in"
height="4.033464566929134in"}

![](media/image27.png){width="7.910416666666666in"
height="5.419444444444444in"}Multi-Filament Model Improves Flux Surface

> Experiments on the W7AS and LHD Stellarators
>
> Have Seen a Soft β Limit

![](media/image28.jpeg){width="3.2333333333333334in"
height="2.2465277777777777in"}

W7AS: German stellarator with *R* = 2 m,

*a* ≤ 0.18 m, 5 periods.

Operated until mid 2002.

Modular coils for W7AS

![](media/image29.png){width="3.6444444444444444in"
height="3.1222222222222222in"}

Variation of 〈β〉 versus injected beam power P~inj~ for (a) ι~vac~(0) =
0.445, B = 0.9 T,

*n*~e~ = 2.4 x 10^20^ m^-3^, *I*~CC~ */ I*~M~ = 0.15 and

\(b\) ι~vac~(0) = 0.575, B = 1.25 T,

*n*~e~ = 1.7 x 10^20^ m^-3^*, I*~CC~ */ I*~M~ *= 0.14.*

> ![](media/image30.wmf)β

![](media/image31.wmf){width="5.339583333333334in"
height="3.689583333333333in"}

![](media/image32.jpeg){width="3.65in" height="3.5409722222222224in"}

![](media/image33.jpeg){width="6.5007874015748035in"
height="2.79251968503937in"}