Radial Electric Field Formation by Charge Exchange Reaction at Boundary of Fusion Device* K.C. Lee U.C. Davis *submitted to Physics of Plasmas

Contents 1.Introduction 2.Assumptions 3.Gyro-center shift - Charge Exchange Reactions - Elastic Scatterings 4.Comparison with Experiments 5.Validity over Quasi-neutrality 6.Conclusion

Introduction  Motive : H-mode transition analysis developed turbulence suppression by ExB flow  Requires the origin of radial electric field : E r  Candidates : Non-ambipolar ion losses [Itoh-Itoh 88’] - Different from experiment [Burrell 89’] Ion orbit loss [Shaing 92’]  There is no commonly agreed theory for E r formation  Experimental research results : ● E r has peak of -30~ -50 kV/m at core periphery near from separatrix within 100 μsec transition time [Burrell 94’ in DIII-D] ● Significant (unknown) correlation between neutrals at edge and H- transition threshold [Carreras 98’ for neutral calculation in DIII-D] Charge exchange with Neutrals => regarded as ‘friction’ in previous works

Assumptions in Theory of Gyro-Center Shift (1)Toroidal and poloidal symmetry except circular gyro motion of ions (1-dimensional approach in radial direction) (2)No transport and MHD activities are included (3)Ionizations, recombinations and electron involved reactions are neglected (electrons are assumed fixed) (4)Semi-Steady state (5)T i =T e =T n Principle of simplicity If we can describe E r by charge exchange and elastic scattering, other considerations can be less important

Concept of Reaction Rate reaction rate density [m -3 s -1 ] R* = σ Φ n n target particle density = neutral density [m -3 ] cross-section (charge exchange) [m 2 ] Incident particle flux = n i v i (ion density)x(ion velocity) [m -3 ][ms -1 ] = [m -2 s -1 ] Reaction rate per ion R [s -1 ] = σ v i n n R [s -1 ] : How many reactions could happen per unit time 1/R [s] : Average time to be taken before reaction

Gyro-Center Shift by Charge Exchange hot ion neutral core boundary

Gyro-Center Shift Calculation average gyro-center shift over (-r L ≤ r ≤ r L ) per reaction x reaction rate of an ion with r L and gyro-center at a point average gyro-center shift rate = σv i ∫rf(r)n n (r)dr σv i ∫f(r)n n (r)dr = (½)r L (n + -n - )/(n + +n - ) (½)σv i (n + +n - ) (¼)σv i r L (n + -n - ) current density (charge separation) different from friction[D’lppolito’02] byand

Gyro Center Shift by Elastic Scattering - asymmetry between backward scattering and forward scattering - scattered angle distribution of s-wave scattering from conservation of energy and momentum (½)σv i r L 2 dn n /dr => new coefficient 0.53 is introduced - only less than 15% due to small cross-section at high temperature

Comparison with Experiments neutral density from Carreras 98’ - emulated data for DIII-D - profiles were made by cubic polynomials except n n - n n has exponential decay into core plasma -separatrix: around R = 2.297m - calculated for three different temperature profiles; a(500 eV), b(400 eV), c(300 eV) - cross section data from Thomas & Stacey 97’(±15%)

Result of Calculation ▫ charge build-up rate [Coul/m 3 sec] showed (-) at core, (+) at SOL

peak dE r /dt value locates around separatrix dE r /dt calculated in infinite slab with many ideal assumptions > ~10 times of experimental value (L/H transient time < 100 μsec) => Profile shape and absolute value are in agreement with experiments

Discussion on the Calculation Results  higher temperature => higher dE r /dt : power threshold of L/H transition ● a scenario of L\H transition L-mode (high turbulence, low E r ) ↓ enough heating + proper neutral distribution => dE r /dt ↑  ExB suppress turbulence flow n e ↑ (pedestal formation) reduce recycling make stiff n n distribution reduce overall n n ↓ dE r /dt ↓( become steady sate with force valence) ↓ H-mode (low turbulence, high E r )

Validity over Quasi-neutrality - electric potential vanishes away out of Debye shielding : screening effect - electric potential is effective inside Debye shielding - when charge build up rate is high enough => all space become field effective - life time of Debye shielding ≡ τ D » electron collision time No. new charges in λ D 3 τ D « 1No. new charges in λ D 3 τ D » 1 Calculated values in the example of experiment are well above the criterion

On the Difference of Charge Exchanges by Gyro-Center Shift and Friction Where, Typical value of J r GCS is 300 times larger than J r F around separatrix Gyro-center shift charge exchange reactions act as cause of the electric field. Friction charge exchange reactions act as retardation of charged particle motion driven by existing electric field.

Miura’92 : neutral energy increase before H α reduction (200~400 μsec), Toda’97 : neutral injection near x-point triggered H-mode(JFT-2M ) Burrell’89 : direction of E r is always inward independent of directions of B T, I P and location of x-point (USN/LSN) Hazeltine’93 : deuteron plasma is easier in H-mode access than hydrogen plasma, Carreras 98’ etc. Supporting Experimental Evidences Conclusion Gyro-center shift by charge exchange reaction => major source of E r formation Future work (1)Simulation : combine ‘gyro-center shift’ with existing edge code (UEDGE, BOUT, etc.) for time transient behavior, poloidal and toroidal aymetryies etc. (2) Experiment : measure/calculate neutral distribution at edge during the L/H- transition → developing a way to control neutral distribution (and H-mode)