# Presentation: 821807

## Recent Progress on QPSD. A. Spong, D.J. Strickler, J. F. Lyon, M. J. Cole, B. E. Nelson, A. S. Ware, D. E. Williamson 

- Improved coil design (see recent Stellarator News article)
- New flux surface optimization target
- Reduced island size
- Invariance of surface shape with 
- Lower cost coils, developable coil winding surfaces
- Neoclassical viscosity/momentum conserving corrections to DKES
- Recent formulation of H. Sugama, S. Nishimura, Phys. Plasmas **9**, 4637 (2002).
- Viscosities depend on the 3 transport coefficients (D11, D13, D33) already calculated by DKES
- QPS poliodal viscosity reduced by a factor of 4-6 over the equivalent tokamak.
- Potential use as an optimization target

## Previous QPS modular coils (January, 2003)

**32 winding packs, 4 distinct coils**

- Two winding packs are joined
- by a structural ‘web’ - requiring
- a single winding form

- 1

- 2

- 3

- 4

- “web coils”

- modular coils

## A re-configuration of the QPS modular coils - together with

**A re-configuration of the QPS modular coils - together with**
**changes in the ****COILOPT**** coil separation targets – has led**
**to a design with improved engineering feasibility and**
**reduced cost**

-  All modular coils are combined in pairs with variable web
-  Number of distinct winding form types reduced from 4 to 3
-  Number of winding packs decreased from 32 to 20
-  Increase min. distance between ‘unpaired’ coils from 9.6 to 13 cm
-  Min. coil radius of curvature increased from 9.3 to > 12.2 cm
-  Min. distance across the center of the torus increased by 4 cm

## A re-configuration of QPS coils

- 1'-1

- 2-3

- 4-5

**A re-configuration of QPS coils**
**reduces the number of modular**
**coil winding form types to 3**

## A new vacuum field constraint in the STELLOPT / COILOPTcode has led to a robust class of Quasi-Poloidal compactstellarator configurations

-  Previously, plasma surface shape/quality was only optimized at the full design 
- No guarantee of good surfaces at low/intermediate ’s
- One could do the optimization at low , but then would lose control over ballooning stability
- Compromise: minimize the normal component of *vacuum* magnetic field error B  = wB|B·n||/|B| using the B field from the coils, but on the *full-pressure* plasma boundary shape.
-  Forces vacuum surface to enclose similar volume as the full-pressure plasma
-  Aspect ratio and shape are maintained as  is increased

## QPS magnetic surface quality improvement

- Full-beta VMEC
- plasma boundary

- Coil winding
- surface

- Full plasma boundary
- and vacuum surfaces of
- QPS PAC configuration

- Full plasma boundary
- and vacuum surfaces of
- new QPS configuration
- before use of the vacuum
- constraint

- Full plasma boundary
- and vacuum surfaces of
- new QPS configuration after use of the vacuum constraint

## Neoclassical viscous flow damping in QPS

- Uses fluid momentum balance equations and friction-flow relations that take into account momentum conservation
- Viscosity coefficients are obtained from the drift kinetic equation
- Uses *l *= 2 Legendre components of f (for which the test particle component of the collision term dominates over the field component)
- Does not directly calculate  and Q from f because the field component of the collision operator is more significant for these moments
- Provides:
- A way to assess viscosities in low aspect ratio quasi-symmetric devices
- Momentum conserving corrections to DKES-based bootstrap currents, particle and energy flows.
- 1H. Sugama, S. Nishimura, Phys. Plasmas **9**, 4637 (2002).
- 2S. P. Hirshman, D. J. Sigmar, Nuclear Fusion **21**, 1079 (1981).

## Relation of viscosities to DKES transport coefficients:

## QPS Viscosities(toroidal damping dominates)

- (poloidal damping dominates)

- QPS Viscosities(toroidal damping dominates)

- Quasi-poloidal symmetry leads to a factor of 4 - 6 reduction in the poloidal viscosity (M’pp) over the equivalent tokamak configuration (at Er = 0, /v = 0.01)

## Collisionality dependence ofQPS viscosities(at edge = 0.5, Er = 0)

**Collisionality dependence of****QPS viscosities****(at ********edge**** = 0.5, E****r**** = 0)**

**E****r**** dependence of QPS viscosity**
**(at ********edge**** = 0.5, ********/v = 0.01)**

## Momentum conserving corrections to DKES particle/energy transport coefficient:

- The parallel viscosity and
- radial flows are given by:

## The formulation of Sugama, et al. is useful for the post-processing of DKES transport coefficients:

- Lowered damping of poloidal flows should allow:
-  Generation of ambipolar transport-driven equilibrium poloidal ExB sheared flows
- Generation of dynamical, Reynold’s stress driven sheared flows possibly at lower power thresholds.
- Both effects can potentially aid in break-up of turbulent eddies (predominantly 2D) allowing access to enhanced confinement regimes
- Development of a poloidal viscosity optimization target
- Momentum conserving corrections to DKES particle/energy transport and bootstrap current coefficients.