SOLF1D and parallel transport in ESEL

motivation of the project - improve calculation of parallel damping terms in ESEL with investigation of parallel transport by SOLF1D code, replace analytic model valid for steady-state simple SOL and couple both codes

ESEL

SOLF1D

SOLF1D

model - Braginskii equations (continuity equation for ions, momentum equation for ions, energy equation for ions and electrons) solved along magnetic field

boundary conditions - sheath boundary conditions

neutrals - fluid model

assumptions - ambipolarity, no net current

cross-field transport - source of mass and energy

SOLF1D

transport equation

ion density

ion momentum

electron energy

ion energy

electron momentum

assumptions

quasineutrality

ambipolarity

Outline

steady state parallel transport - parallel damping in SOLF1D and ESEL compared for steady state

transient parallel transport - application of SOLF1D to fluctuations calculated in ESEL

• one peak only

• series of fluctuations

averaging - errors associated with averaging of plasma parameters estimated for data from ESEL

• calculated at outer mid-plane

• will be studied also along the SOL

Parallel losses in steady state

parallel density loss time parallel energy loss time

analytic model

analytic model - parallel damping terms as a function of n, Te and L|| based on subsonic advection and Spitzer-Härm diffusion and L|| = Lc

conclusions - approximation for temperature ok, density model too crude - neutrals important in steady state, not simple SOL, L|| Lc

Simple time-dependent case

cross-field sources of particles and energy in time

cross-field sources of particles and energy in parallel direction

Simple time-dependent case

steady-state solution

cross-field sources plasma parameters parallel losses

Simple time-dependent case

temporal profiles

cross-field sources mid-plane values target values parallel losses

Simple time-dependent case

parallel losses

parallel loss times parallel losses conduction and convection contribution

Simple time-dependent case

parallel transport

parallel profiles plasma velocity

Simple time-dependent case

parallel transport

plasma density

Time-dependent case with ESEL data

case 1 - cross-field sources on input (initial condition is steady state for average values of sources)

plasma parameters parallel losses cross-field sources

Time-dependent case with ESEL data

case 1 ESEL

SOLF1D

Time-dependent case with ESEL data

case 2 - density and temperature on input (cross-field source adjusted to obtain specified density and temperature)

Time-dependent case with ESEL data

case 2 ESEL

SOLF1D

Time-dependent case with ESEL data

case 2 ESEL

SOLF1D

Time-dependent case with ESEL data

case 2

parallel losses

Time-dependent case with ESEL data

sources of particles and energy as input

case 1 - density and temperature in SOLF1D can differ from ESEL

- density and temperature must be limited in some range

density and electron temperature as input

case 2 - density and electron temperature copy ESEL values

- ion temperature not stable, probably due to coarse grid

- additional loop to find sources in each iteration

conclusions - energy transport dominated by diffusion, T tends to flatten fast

and assumption L|| = Lc more appropriate than for n

- dominant source from the mid-plane in transient case,

processes at target not as relevant as in steady state

next step - parametrization ?

Averaging

data results from ESEL at 4 radial positions

results - errors associated with averaging of plasma parameters calculated as

Averaging

next steps

- effect in parallel direction

- compare steady-state result

taking average values and

time-dependent case

- effect on detachment