A Hybrid Inductive Scenario for a Pulsed- Burn RFP Reactor with Quasi-Steady Current. John Sarff

A Hybrid Inductive Scenario for a Pulsed- Burn RFP Reactor with Quasi-Steady Current John Sarff 12th IEA RFP Workshop Kyoto Institute of Technology, Kyoto, Japan Mar 26-28, 2007

The RFP fusion development path depends strongly on the method used to sustain the plasma current. Integration of efficient current drive with reactor-relevant confinement is very challenging, perhaps defining the RFP s highest priority fusion development issue. Inductive current drive is pulsed (except for Oscillating Field Current Drive) What is the COE penalty for a pulsed versus steady-state system? Is this penalty smaller for a low toroidal field system? Prospects for non-inductive current drive: Pressure-drive current would help, but the implied high β may be challenging RF or neutral beams for full sustainment are too inefficient but a small amount for current profile control might be affordable

Possible scenarios. Baseline scenario uses Oscillating Field Current Drive (viz. TITAN) Steady-state Inductive current drive efficiency very low re-circulating power fraction Competitive COE compared to tokamak system studies Requires dynamo-relaxation process that is consistent with good confinement Conventional long pulse inductive Gives up steady-state, surely increasing the COE Confinement improvement via single-helicity dynamo or auxiliary noninductive current drive may be essential Method for the Standard RFP database Pressure-driven bootstrap current would help But it cannot provide all of the required current Steady-state, with non-inductive residual current drive Requires stability and good confinement at very high β ~ 100% Achievable only at low aspect ratio R/a?

This talk explores another scenario: combining a PPCD-like pulsed-burn phase with an OFCD current re-build. Addresses concerns that: dynamo sustainment with simultaneous high confinement may not be possible even partial non-inductive current drive could be too inefficient Hybrid scenario is fully inductive and efficient, even during the non-burn phase. Current never goes to zero, reducing mechanical and thermal stresses relative to conventional pulsed current scenario. Capitalizes on improved confinement in dynamo-free periods already being demonstrated in our experiments. Capitalizes on dynamo-relaxation, but only for current drive ease and efficiency.

Inductive hybrid: a dynamo-free period (self-similar ramp-down and PPCD) followed by a current re-build using OFCD. Some issues impacting this hybrid scenario s attractiveness: How much larger will the plasma current need to be What is the optimum duty-cycle (physics and/or engineering) Is a larger minor radius, a, preferred How much larger is the re-circulating power fraction I p (t) I p ~ I 0 e "t /# ssrd OFCD re-build " ssrd # 0.1" R dynamo-free improved τ E " R = µ 0 a 2 /$ # 2000a 2 [s] Time (hybrid cycles)

Outline. The hybrid cycle and its ingredients. Modeling of the time-average fusion power and Ohmic heating Test the sensitivity of parameters Quantify the cycle extremes Identify an optimum Goal to create specifics for system study optimization, likely to have additional constraints to those discussed here.

Mini review of self-similar ramp-down. Space-time separable solutions of magnetic diffusion Magnetic equilibrium constant in time, e.g., stationary safety factor q(r) Dynamo-free Ohm s law improved confinement %" E + V " B = #J $ & 'B 't + % " ( V " B & # + * % " B- = 0 ) µ 0, with { B = b(t) B(r) [",V]= a(t) ["(r),v(r)] " = #b/#t = separation constant a(t)b(t) Time dependence b(t) = b(0)e " $ a( t #)d t # = b(0)e "at if η(t) = constant Example: V,"# = 0 t 0 (e.g., burning plasma) " #B #t = $ % & (% & B) = $'2 B µ 0 µ 0 " b(t) = b(0)e #(a$ )2 t /% R " # B = $ B " ssrd ~ " R /10 Gimblett et al., 83 ; Nebel et al., PoP 02

OFCD scales favorably to high Lundquist number. "I # I # 100% OFCD S "1/4 Toroidal current modulation scales as ~ S 1/4 from reactive impedance (see Ebrahimi et al, PoP 03) "F (~ "I tf ) negative extrema standard range PPCD range Large, cyclic equilibrium modulation for S < 10 6 ZT40 MST Reactor S = " R /" A

Ramp-down is essential to avoid magnetizing flux accumulation, but the optimal loop voltage programming is unknown. During the ramp-down, the toroidal loop voltage must satisfy: "# mag = % V $ (a) dt & 0 Note: magnetizing flux easily nulled by partial ramp steady induction during the OFCD re-build Optimal loop voltages likely determined by MHD tearing stability and residual transport controlling the resistivity profile, η neo (r) Self-Similar Ramp Down PPCD ( Pure Poloidal ) I φ E φ I φ E θ E θ I θ E φ I θ Time (arb) Time (arb)

Ramp-down is essential to avoid magnetizing flux accumulation, but the optimal loop voltage programming is unknown. During the ramp-down, the toroidal loop voltage must satisfy: "# mag = % V $ (a) dt & 0 Note: magnetizing flux easily nulled by partial ramp steady induction during the OFCD re-build Optimal loop voltages likely determined by MHD tearing stability and residual transport controlling the resistivity profile, η neo (r) Self-Similar Ramp Down PPCD ( Pure Poloidal ) I φ E φ I φ E θ E θ I θ E φ target in common I θ Time (arb) Time (arb)

Simple model for the hybrid cycle used to estimate time-average fusion power, Ohmic heating power, Q, etc Fusion power scaling for the RFP P fusion ~ n 2 a 2 R ~ " 2 B 4 a 2 R ~ " 2 I 4 R a 2 (constant T e,i = 10-20 kev) Q = P fusion P " ~ # 2 I 2 (assuming Ohmic heating) Model for the hybrid cycle "P fusion # ~ I 0 4 & T ramp T tran I p (t) e $4t /% ssrd T ramp + I 0 (1$ e$t ramp /% ssrd ) (di /dt) 14 42 4 ofcd 443 re-build time I 0 T tran ~ τ E (?) T ramp transition time I ~ e "t /# ssrd (P fusion = 0) re-build time (P fusion = 0)

About a 10% larger peak plasma current is required for the same fusion power with respect to steady-state (e.g., TITAN). "P fusion # hybrid I 0 4 ~ (P fusion ) ss 1 sec T tran = 0 sec 10 sec Hybrid parameters used: ramp-down (a = 1 m) " ssrd = 0.1" R = 200 sec OFCD re-build " I 0 % $ ' # di /dt & ofcd = 5 sec I 0 1/4 "P fusion # hybrid 1 sec 10 sec T tran = 0 sec T ramp /" ssrd

Average Ohmic heating power depends most on the electron temperature confinement during the OFCD ramp. (T e is value during re-build) Concern: "P # $ hybrid I 0 2 ~ (P # ) ss 5 kev 2 kev T e = 15 kev T e 10 kev during burn but T e << 10 kev during re-build Q = "P fusion # I 0 2 "P $ # 5 kev 2 kev T e = 15 kev T tran = 1 sec T ramp /" ssrd

Average Ohmic heating power depends most on the electron temperature confinement during the OFCD ramp. Maximum Q implies the optimum duty-cycle T ramp / τ ssrd = 0.1-0.2 "P # $ hybrid " I 0 % $ ' # di /dt & ofcd " I 0 % = 5 sec $ ' = 20 sec # di /dt & ofcd I 0 2 ~ (P # ) ss 5 kev 2 kev T e = 15 kev 5 kev T e = 15 kev 2 kev Q = "P fusion # I 0 2 "P $ # 5 kev 2 kev T e = 15 kev 5 kev 2 kev T e = 15 kev T tran = 1 sec T tran = 1 sec T ramp /" ssrd T ramp /" ssrd

Existing Standard RFP scaling is favorable for efficient OFCD. Last look at standard RFP parameter scaling in MST T e (0) ~ I 0.67 p ( I p /N) 0.5 M. Stoneking et al, PoP 98 Project to high current: Pick lower density end of I p / N range to maximize the electrical conductivity Size scaling less known, but TITAN s minor radius is only a = 0.6 T e (0) (ev) 400 ev TITAN-sized (0.5/0.6)*18 MA 4 kev MST 0.5 MA I p / N = 6 10 14 A-m I p (MA)

Hybrid cycle for maximum Q, in real time units. Pulsed-burn rate is much faster than conventional pulsed In PULSAR, the shield-blanket included thermal storage to buffer a 200 s nonburn period (while the magnetizing transformer was reset) Parameters: T e (0) = 15 kev, a = 1 m I p " ssrd = 0.1" R = 200 s Normalized P fusion P fusion T ramp = 0.15" ssrd = 30 s I(dI /dt) #1 = 5.5 s T tran = 1 s (OFCD detail not illustrated) Time (s)

Summary. Integration of the current sustainment and reactor-grade confinement is critical for the RFP as a fusion concept Best scenario could still be OFCD, if fusion-relevant confinement is achieved Must re-assess pulsed or hybrid scenarios to quantify negative impact on reactor attractiveness Steady-state bootstrap + non-inductive J(r) control an emerging path? A hybrid scenario for pulsed-burn in rapid cycles of dynamo-free current rampdown and OFCD re-build might be nearly as attractive as steady-state OFCD Simple and efficient current drive applied at the boundary Could reduce deleterious pulsed-system challenges (relative to the conventional pulsed on-off scenario) Perhaps more robust extrapolation of established RFP science Integration analysis of more elements needed to expose other issues impacting RFP reactor attractiveness, i.e. resistive wall mode control, boundary, particle control, etc