Operational Phase Space of the Edge Plasma in Alcator C-Mod

Operational Phase Space of the Edge Plasma in B. LaBombard, T. Biewer, M. Greenwald, J.W. Hughes B. Lipschultz, N. Smick, J.L. Terry, Team Contributed talk RO.00008 Presented at the 47th Annual Meeting of the APS Division of Plasma Physics October 4-8, 005 Denver, Colorado

The operational space of the edge plasma that is accessible to experiments is restricted......one can not 'dial up' arbitrary n, Te values and gradients Instead, robust SOL profiles are observed, primarily set by 'external' machine control parameters (Ip, ne) 0 0 m - 0. SOL Density Profiles Near SOL Far SOL 0. 0.5 = n e /n G -5 0 5 0 5 0 5 Distance into the SOL (mm) Observations: Far SOL - Intermittent transport events - Rapid ExB advection towards walls Near SOL - Steep gradients - Flux-gradient transport paradigm appropriate?

Transport near the separatrix may be described in terms of EMFDT, the basis for first-principles -D transport simulations Physics: ElectroMagnetic ~ parallel inductance, finite B, parallel resistivity, Fluid Drift non-linear drift-wave, curvature, -D Turbulence "ballooning-like" asymmetries, x-point effects Turbulence character & transport level determined primarily by two dimensionless parameters Inverse / / 4 Poloidal P a Collisionality Beta Gradient MHD ~ q R ^ a d ~ l ei R q ( Parameter R ) ( L n) B [] Scott, PPCF 9 (997) 65. [] B. Scott [] Xu, X.Q., et al., Nucl. Fusion 40 (000) 7. [4] Rogers, Drake, and Zeiler, Phys. Rev. Lett. 8 (998) 496.

Transport near the separatrix may be described in terms of EMFDT, the basis for first-principles -D transport simulations Physics: ElectroMagnetic ~ parallel inductance, finite B, parallel resistivity, Fluid Drift non-linear drift-wave, curvature, -D Turbulence "ballooning-like" asymmetries, x-point effects Turbulence character & transport level determined primarily by two dimensionless parameters Inverse / / 4 Poloidal P a Collisionality Beta Gradient MHD ~ q R ^ a d ~ l ei R q ( Parameter R ) ( L n) Electron Heat Diffusivity [] 0 c e 0 B 0 0 I 0-0 - 0 - a 0 0 MHD => strong dependence on for > 0. [] Scott, PPCF 9 (997) 65. [] B. Scott [] Xu, X.Q., et al., Nucl. Fusion 40 (000) 7. [4] Rogers, Drake, and Zeiler, Phys. Rev. Lett. 8 (998) 496.

Transport near the separatrix may be described in terms of EMFDT, the basis for first-principles -D transport simulations Physics: ElectroMagnetic ~ parallel inductance, finite B, parallel resistivity, Fluid Drift non-linear drift-wave, curvature, -D Turbulence "ballooning-like" asymmetries, x-point effects Turbulence character & transport level determined primarily by two dimensionless parameters Inverse / / 4 Poloidal P a Collisionality Beta Gradient MHD ~ q R ^ a d ~ l ei R q ( Parameter R ) ( L n) Electron Heat Diffusivity [] 0 B 'Phase Space' of EMFDT [4] c e 0 0 0 I 0-0 - 0 - a 0 0 MHD => strong dependence on for > 0. Inaccessible Transport Increasing a d <= increasing collisionality transport depends on location in (, a d ) 'phase-space' [] Scott, PPCF 9 (997) 65. [] B. Scott [] Xu, X.Q., et al., Nucl. Fusion 40 (000) 7. [4] Rogers, Drake, and Zeiler, Phys. Rev. Lett. 8 (998) 496.

Hypothesis: Edge operational phase space is set by EMFDT, combined with particle & power balance constraints a) Transport is a strong function of EMFDT 'control parameters' / / 4 P ~ q R ^ ; a d ~ l ei R q ( R ) ( L^) B b) Heat fluxes set by input power, particle fluxes set by fueling lines of ~constant heat flux "critical gradient" Electron Heat Diffusivity 0 c e 0 0 0 I increase x 00 Experimental Test: 0-0 - 0 0 Edge plasma states that are accessible to experiments should ~map to the two-parameter 'phase-space', ~ P q R ^ B a d ~ 0 - edge plasma state restricted to this band ( ) / / 4 R q L^) independent of machine parameters (B T, Ip, ne) ; R l ei (

Results from 000 campaign: Plasma states near separatrix are indeed found to occupy a well-defined region in the phase space of EMFDT Discharges with different machine parameters: BT, Ip, ne 6 = 6.5 BT (tesla) 5 4 = 5 =.5 0.4 0.6 0.8 Ip (MA) Low-power Ohmic L-mode discharges Density: 0.4 < n/n G < 0.5 Lower single-null Forward Ip, BT to be published in Nuclear Fusion.

0. 0 0. 0.4 0.6 0.8 Results from 000 campaign: Plasma states near separatrix are indeed found to occupy a well-defined region in the phase space of EMFDT Discharges with different machine parameters: BT, Ip, ne...occupy in a similar band in, a d space BT (tesla) 6 = 6.5 5 4 = 5 =.5 ~ nt e B ~ p e I p q R L p e. 0.8 0.4 Inaccessible I P (MA) 0.8 0.5 0.4 0.6 0.8 Ip (MA) Low-power Ohmic L-mode discharges Density: 0.4 < n/n G < 0.5 Lower single-null Forward Ip, BT 0.0 0.0 0. 0.4 0.6 0.8 ~ / / 4 Ê l Á ei ˆ Ê R ˆ a d Á q Ë R Ë L n <== increasing ne A region of high at high density is inaccessible, owing to an explosive growth of cross-field transport to be published in Nuclear Fusion.

- 0 4 5 6-0 4 5 6 Pressure gradients near the separatrix appear to clamp at similar values of when normalized collisionality is held fixed Look at pressure profile data from discharges with ~ 0.5, mm from separatrix BT (tesla) 6 = 6.5 5 4 a d = 5 =.5 0 0 ev m - mm - 0 0 0 0 nt e ^ nt e ^ 0 I P (MA) 0.8 0.5 B T (T) 6 5 4 0.4 0.6 0.8 Ip (MA) 0. 0 4 6 Distance from into SOL (mm)

- 0 4 5 6-0 4 5 6 Pressure gradients near the separatrix appear to clamp at similar values of when normalized collisionality is held fixed Look at pressure profile data from discharges with ~ 0.5, mm from separatrix BT (tesla) 6 = 6.5 5 4 a d = 5 =.5 0.4 0.6 0.8 Ip (MA) I p Scan: Pressure gradients scale roughly as I p => similar 0 0 ev m - mm - 0 0 0 0 nt e ^ nt e ^ 0. 0 4 6 Distance from into SOL (mm) 0 I P (MA) 0.8 0.5 B T (T) 6 5 4

- 0 4 5 6-0 4 5 6 Pressure gradients near the separatrix appear to clamp at similar values of when normalized collisionality is held fixed Look at pressure profile data from discharges with ~ 0.5, mm from separatrix BT (tesla) 6 = 6.5 5 4 a d = 5 =.5 0.4 0.6 0.8 Ip (MA) I p Scan: Pressure gradients scale roughly as I p => similar B T Scan: No sensitivity to toroidal field 0 0 ev m - mm - 0 0 0 0 nt e ^ nt e ^ 0. 0 4 6 Distance from into SOL (mm) 0 I P (MA) 0.8 0.5 B T (T) 6 5 4 => Pressure gradient near separatrix set by a 'critical poloidal beta gradient'

New Experiments (005) - Further tests of the 'phase-space' concept for the Near SOL Extended range of Ip, BT 6 = 6.5 BT (tesla) 5 4 = 5 =.5 0.4 0.6 0.8 Ip (MA) Density scans: 0. < n/n G < 0.5 with lower currents (0.4 MA) and fields (4,.=>.7 tesla) Improved scanning probe diagnostics

New Experiments (005) - Further tests of the 'phase-space' concept for the Near SOL Extended range of Ip, BT Lower vs upper-null topologies 6 = 6.5 BT (tesla) 5 4 = 5 =.5 0.4 0.6 0.8 Ip (MA) Density scans: 0. < n/n G < 0.5 with lower currents (0.4 MA) and fields (4,.=>.7 tesla) co-current rotation drive counter-current rotation drive SOL flows change dramatically with X-point location; suggested link to L-H power threshold differences Improved scanning probe diagnostics Nucl. Fusion 44 (004) 047.

New Experiments (005) - Further tests of the 'phase-space' concept for the Near SOL Extended range of Ip, BT Lower vs upper-null topologies 6 = 6.5 BT (tesla) 5 4 = 5 =.5 0.4 0.6 0.8 Ip (MA) Density scans: 0. < n/n G < 0.5 with lower currents (0.4 MA) and fields (4,.=>.7 tesla) Improved scanning probe diagnostics Nucl. Fusion 44 (004) 047. co-current rotation drive counter-current rotation drive SOL flows change dramatically with X-point location; suggested link to L-H power threshold differences What is influence on SOL 'phase-space'? => Run matched discharges with upper and lower null

New Results (005) - Pressure gradients near sep. consistently scale as Ip... but value depends on lower / upper X-point topology 0.8 MA nt e ^ 0 4 ev m - mm - nt e ^ 0 0.4 MA 0.8 MA 0.4 MA 0 0. 0. 0. 0.4 0.5 0.6 R l ei / q ( ) Ê L ~ n ˆ a d Á Ë R / 4

New Results (005) - Pressure gradients near sep. consistently scale as Ip... but value depends on lower / upper X-point topology nt e ^ 0.8 MA Edge plasma states again align in EMFDT phase-space, but in two bands 0 4 ev m - mm - nt e ^ 0 0.4 MA 0.8 MA 0.8 0.6 0.4 0. 0.4 MA 0 0. 0. 0. 0.4 0.5 0.6 R l ei / q ( ) Ê L ~ n ˆ a d Á Ë R / 4 0.0 0. 0. 0. 0.4 0.5 0.6 R l ei / q ( ) Lower null achieves higher peak values of compared to upper null

Plasma flows in the SOL are dramatically different in Lower vs Upper null topologies... perhaps affecting the attainable values of High-field side SOL r = mm 0.5 0.0 Parallel Flow Mach Number -0.5-0. 0. 0. 0.4 0.5 0.6 R l ei - Plasma flows from low to high-field side (ballooning-like transport drive) / q ( )

Plasma flows in the SOL are dramatically different in Lower vs Upper null topologies 0.5... perhaps affecting the attainable values of High-field side SOL r = mm 0.4 Low-field side SOL Parallel Flow Mach Number r = mm 0.0-0.5 Parallel Flow Mach Number 0. 0.0-0. 0. 0. 0.4 0.5 0.6 - Plasma flows from low to high-field side (ballooning-like transport drive) / q ( ) R l ei 0. 0. 0. 0.4 0.5 0.6 R l ei / q ( ) - Low-field side flows near sep. are affected (~toroidal rotation)

Plasma flows in the SOL are dramatically different in Lower vs Upper null topologies 0.5... perhaps affecting the attainable values of High-field side SOL r = mm 0.4 Low-field side SOL Parallel Flow Mach Number r = mm 0.0-0.5 Parallel Flow Mach Number 0. 0.0-0. 0. 0. 0.4 0.5 0.6 - Plasma flows from low to high-field side (ballooning-like transport drive) / q ( ) R l ei - Low-field side flows near sep. are affected (~toroidal rotation) -0. 0.8 0.6 0.4 0. - Highest is achieved when flow is positive (co-current) on low-field side => favors lower null topology (Note: lower null also has lowest L-H threshold power) 0.0 0. 0. 0. 0.4 0.5 0.6 R l ei / q ( ) r = mm

Summary Operational space of edge plasma states (density, temperature, gradients) in C-mod is highly constrained...yet sensitive to machine control parameters (Ip, ne) Behavior may be understood in terms of Electromagnetic Fluid Drift Turbulence Near SOL plasma 'self-organizes' towards a ~critical poloidal beta gradient ( ); attainable depends on collisionality ~ a d Accessible edge states map to a -D dimensionless 'phase space' (, ) Mapping is invariant of machine parameters for fixed magnetic topology: 0.4 < Ip < MA,.7 < B T < 6T, 0. < ne/n G < 0.5 Lower null topology leads to higher than Upper null Equilibrium plasma flows near the separatrix are also different Co-current plasma flows in the SOL are associated with higher => Flow is another phase space parameter (,, M,...) a d Observations make contact with L-H power threshold being lower in Lower null a d