Ignited Spherical Tokamaks and Plasma Regimes with Liwalls, L. E

Fusion Engineering and Design 72 (2004) 149–168

Ignited spherical tokamaks and plasma regimes with LiWalls

L.E. Zakharova,∗, N.N. Gorelenkova, R.B. Whitea, S.I. Krasheninnikovb, G.V. Pereverzevc

a Princeton Plasma Physics Laboratory, MS-27, P.O. Box 451, Princeton, NJ 08543-0451, USA b University of California, San Diego, Energy Research Center, La Jolla, CA 92093, USA c Max-Plank-Institute f¨ur Plasmaphysik, D-85748 Garching bei M¨unchen, Germany

Available online 13 October 2004

Abstract Basic requirements of the fusion power reactor and its development are outlined. The notion of operational power reactor regime (OPRR) is introduced explicitly for the first time in order to distinguish it from the relatively short ignition phase of the reactor operation. Development of OPRR is intrinsically linked to two basic technology objectives, i.e., development of the first wall (FW) and the tritium cycle (TC). The paper reveals an existing fundamental gap in the reactor development path associated with the lack of necessary amounts of tritium for the reactor design development. In this regard, low recycling regimes with a plasma limited by a lithium wall surface suggest enhanced stability and energy confinement, both necessary for tokamak power reactors. These regimes also could make ignition and OPRR feasible in compact tokamaks. Ignited spherical tokamaks (IST), self-sufficient in the bootstrap current, are introduced as a necessary interim step for development OPRR-FW-TC for the power reactors. © 2004 Elsevier B.V. All rights reserved.

PACS: 28.52-s; 28.52.Av; 28.52.Cx; 52.55.Fa; 52.55.-s; 52.55.Tn

Keywords: Tokamaks; Fusion reactor; Ignition; First wall; Tritium; DD fusion

1. Introduction Burning and ignition can be achieved and demon- strated with essentially conventional plasma regimes. At present, tokamak research is entering a new phase An enhancement of size, magnetic field (together with α when the fusion produced -particle heating will dom- the cost of the machine) are required. Although not inate over the external input of energy into the plasma yet envisioned, a short ignited phase, probably, can [1]. Still there will be, at least, two more phases on be achieved in the next generation of toka-maks, like the road to a reactor after this “burning”, sub-critical ITER, with a modest improvement of confinement. plasma development. They include demonstration of On the other hand, power production needs a ignition, and development of the regime and associ- special regime, called here an operational power ated technology for power production. reactor regime, or OPRR. OPRR requires 4–5 times higher power density than ignition and needs a plasma ∗ Corresponding author. Tel.: +1 609 243 2630; fax: +1 609 243 2662. with significantly enhanced stability and confinement E-mail address: [email protected] (L.E. Zakharov). properties.

The conventional tokamak regimes have a peaked Only compact, spherical tokamaks (ST) are suitable plasma temperature as their most prominent charac- for this purpose. Even though relatively small, these teristic. With high recycling at the plasma edge, and devices still should be self-sufficient in tritium and apparently producing plasma edge consistent with the breed it with 100% efficiency or even more. Moreover, material surfaces, this feature, at the same time, leads in order to use the entire wall surface for breeding to substantial consequences limiting the tokamak core ignition is a necessary condition to allow filling all performance: turbulent energy losses [2], degradation NBI ports with a tritium breeding material after of confinement with the power [3], Troyon limitations ignition has been reached. of plasma beta [4,5], possibility of sawtooth relaxations A possible candidate for a mission of FW develop- and internal collapse [6], instabilities at high edge den- ment could be an ignited spherical tokamak (IST), dis- sity [7], etc. cussed further in this paper. The high beta (β>40% The second characteristics is that a conventional and 35% achieved already) compensates a relatively plasma is separated from the stabilizing wall surface by small magnetic field, only possible for ST. At the same a “vacuum” gap, and, thus, is prone to free boundary time, the problem of non-inductive current drive should MHD instabilities, which further reduce the stability be solved for ST. Conventional plasma regimes cannot margins. As a result, stability, confinement degrading provide sufficient confinement, fusion power density with the power, and overall performance remain insuf- and bootstrap current for an IST. Thus, with the con- ficient for a power reactor. ventional plasma there is a gap on the development path This paper emphasizes that the search for new to a reactor (even with use of high magnetic fields or plasma regimes in tokamaks is unavoidable for devel- low aspect ratio). opment of a magnetic fusion reactor. Enhancement in The alternative could be a low recycling plasma with stability and confinement are two of the requirements. high edge temperature, which would correspond to an- A fusion reactor requires a certain level of plasma other class of confinement and stability regimes. Good pressure (0.8–1 MPa) for power production. For mag- plasma pumping by a lithium surface opens the pos- netic fields B 5 T such a pressure corresponds to beta sibility for a high temperature pedestal. If combined values of 8–10 %. For aspect ratios R/a > 3 (determined with core fueling, it creates a new confinement regime, by shielding from neutrons and radiation) conventional where energy losses are determined by the particle dif- regimes with peaked plasma temperature are limited by fusion, rather than by thermo-conduction. In contrast much lower stability margins, e.g., β = 2.7% in ITER, to thermo-conduction, diffusion is ambipolar and, thus, probably, β 4% in future, which are too small for a the losses are determined by the best confined plasma power reactor. species. As a result, better confinement is expected in Hypothetically, at higher magnetic fields, e.g., B the low recycling regime. 7.5 T, the conventional regimes can approach the re- At the same time, a lithium surface allows for a actor plasma pressure even with moderate β 4%. conducting (back up) wall situated right at the plasma The problem is (besides numerous technological is- boundary, thus, potentially eliminating free boundary sues) that the experimental data base for stability mar- instabilities. This would be a crucial improvement al- gins at high fields will remain absent until fusion power lowing not only approaching the OPRR stability re- will be used at full extent for the plasma heating. Also, quirement, but also leading to smaller and less costly fast degradation of the energy confinement τE with the experiments. −αP heating power P, i.e. τ ∝ P , αP > 0.5 in conven- It is shown in this paper that with high edge tem- tional plasma precludes reaching OPRR af-ter plasmas perature, the ignition and stationary regimes in ST have been ignited. seem to be possible. ISTs could be unique devices for The second reason is limited availability of tritium. developing the physics and technology of the power The development of the first wall (or FW, considered reactor. here as the first 10–15 cm of material structure faced Section 2 of the paper summarizes the basic re- by fusion neutrons) would require consumption of quirements of the reactor development and motivation a large amount of tritium (about 1 kg/m2 for accu- for new plasma regimes. Section 3 discusses the ba- mulating the neutron fluence of 15 MW-year/m2). sic transport properties of the LiWall regime. Section 4 L.E. Zakharov et al. / Fusion Engineering and Design 72 (2004) 149–168 151 outlines the particle and energy extraction capabilities 2.1. Ignition criterion of LiWalls. Section 5 explains the stability enhancement for LiWall limited plasma. Section 6 discusses A fusion reactor should be able to reach the IST stabilty, self-sufficiency of bootstrap current, and “ignition” condition when the energy losses are com- stabilization of micro-turbulence. pensated by the fusion alpha particle heating Epl = f␣ P␣ dV, P␣ = E␣nDnTσvDT, (1) 2. Basic physics and technology aspects of the τ¯E fusion reactor Epl Epl ≡ + Prad dV, (2) Among numerous issues there are three specific ob- τ¯E τE jectives of magnetic fusion which should be developed E for the fusion reactor where pl is the total plasma energy integrated over plasma volume V , P␣ the density of the alpha particle power, E␣ = 3.5 MeV, nD,nT are the densities of (1) Ignition and operational power reactor regime deuterium and tritium, respectively, and σv is the (OPRR). DT cross-section of the reaction. The coefficient f␣ reflects (2) Design of the low activation first wall (FW) to- the direct losses of the ␣-particles. In Eq. (2) the en- gether with power extraction and helium ash ex- ergy confinement time τ¯E (with a bar) takes into account haust. all energy losses from the plasma, including radiation (3) Tritium cycle (TC). power Prad, while, typically, the definition of τE ex- cludes the radiation. When existing plasma physics results together with Because the cross-section of the DT reaction within technology and economic aspects are taken into ac- the known accuracy is proportional to the plasma tem- count, the development of the fusion reactor appears to perature squared T 2 [8], the appropriate scaling for the be rather restricted by fundamental constraints. Thus, volume averaged alpha particle power can be written as a clear distinction should be drawn between the ignition phase (with low plasma beta and high energy 1 2 P␣ dV = C␣4pDpT=p fpkC␣, (3) confinement) and continuous OPRR (with high beta V0 and reduced energy confinement). In its turn, the very P␣ 4pDpT development of OPRR requires use of fusion power C␣ ≡ ,f≡ , (4) p p pk p2 for reaching the necessary plasma parameters and for 4 D T stability limit studies. where · stands for volume averaging, V0 the to- Use of fusion power is extremely restricted by lim- tal plasma volume, p, pD,pT the correspondingly itations on tritium consumption (besides many other plasma, deuterium and tritium ion pressures, respec- technology and safety aspects). As a result, the physics tively. The coefficient C␣, which depends on T, pD,pT and technology of OPRR, power extraction, FW and profiles, is referred here as a reactivity factor. The TC should be first developed on compact devices, rather “peaking” factor fpk takes into account peakedness than on the reactor scale machines. In a comparison of of the plasma pressure profile, dilution of DT mix by two approaches for compact ignition, i.e., use of high helium ash and by impurities, and the difference in magnetic field or high-beta spherical tokamaks, Ignited electron and ion temperatures. In the low recycling STs have a crucial advantage in being able to use up regime the content of impurities and contribution of to 90% of neutrons for breeding. Their central rod has hot ␣-particle pressure can be made small. a relatively small space view angle for neutrons, thus, The value of C␣ can be calculated for different den- leaving most of the space around the plasma available sity and temperature profiles. Here, we introduce the for breeding materials. reference normalized profiles shown in Fig. 1a This section explains the necessity of high-beta and s V¯ ≡ + ν − V¯ ν,nV =n s V¯ , ignited spherical tokamaks (IST) for the development ν( ) (1 )(1 ) e( ) e νn ( ) of reactor physics and technology. (5) 152 L.E. Zakharov et al. / Fusion Engineering and Design 72 (2004) 149–168

Fig. 1. (a) Reference profiles (with the same volume averaged values) for plasma density and temperature. (b) C␣ as a function of averaged plasma temperature. The red curve for νT = 0 does not depend on νn = 0–2. Blue curves correspond to νn = 0 and νT = 0.25–2. (c) C␣ for another set of profiles. Red curves are for νT = 0.25 with νn = 0.25–2, and blue curves are for νn = 0.25 with νT = 0.25–2. For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.

PX−ray dV [9] in the same form as C¯ ␣ T V =T s V¯ , ( ) νT ( ) (6) 1 C¯ X ≡ P V. where V¯ ≡ V/V0 is the normalized plasma volume. 2 X-rayd (8) p Zeff V0 Each pair of density and temperature profiles can be referenced by a double index (νn,νT ). The Bremsstrahlung radiation is proportional to Zeff Fig. 1b and c show the fusion reactivity factor C␣ for and for Zeff = 1 constitutes less than 10% of the ␣- two sets of profiles each. The red curves corresponds power for the optimum temperatures. to flat and “almost flat” temperature profiles of the low The ignition criterion (2) can be now written recycling regime, while blue ones to the high recycling as regimes with flat or “almost flat” density. While there 3 p 2 1 is a significant dependence of the C␣ factor on the aver- = f␣P␣, C␣pτ¯E = . (9) 2 τ¯ 3 f␣f aged temperature, its maximum value for each profile E pk is almost the same for different profiles. The optimum The pressure peaking factor fpk, which for reference C¯ value, which we refer as ␣, as a function of temper- profiles depends on the sum νn + νT , is shown in ature peaking index νT for different density profiles is Fig. 2b. For the optimum choices of the plasma tem- shown in Fig. 2a. With good accuracy peratures (7), the ignition criterion is reduced to MW f pf τ = f pτ∗ = , C¯ ␣ 1.5 . (7) pk ␣ ¯E 1or pk ¯E 1 (10) MPa2 ∗ where the abbreviation τ¯E ≡ f␣τ¯E is introduced to ab- Note that this optimum value can be achieved only in sorb the factor f␣. The same criterion can be written in a stationary regime. Any plasma profile oscillations equivalent forms in time would make the operational C␣ smaller than f n T τ∗ = × 20, C¯ ␣. pk e ¯E 31 10 For comparison Fig. 2a shows also an analogous ∗ 2µ p f βB2τ¯ = 2.5,β≡ 0 , (11) factor C¯ X expressing the Bremsstrahlung radiation pk E B2 L.E. Zakharov et al. / Fusion Engineering and Design 72 (2004) 149–168 153

Fig. 2. (a) Optimum reactivity factor C¯ ␣ of alpha particles and Bremsstrahlung radiation factor C¯ X (Zeff = 1) for different reference density and temperature proﬁles (νn=0–2,νT =0–2) at optimum plasma temperature. (b) Pressure peaking factor for reference proﬁles.

−3 where ne is the plasma density in [m ], and T is from the plasma. On the path to the reactor, the burning in [keV]. In practice (e.g., ITER applications) another plasma has a very limited potential contribution to the form, written in terms of central values of plasma den- reactor development. sity n0 and temperature T0 (assuming some particular 2.2. Operational Power Reactor Regime factors f␣,fpk), 20 At the optimum temperature, the total fusion power n0T0τE = 50 × 10 (12) of the reactor is proportional to the plasma pressure is in use (with conventional τE not accounting for the squared radiation). 2 Ignition criterion (10) should be fulfilled during both PDT = 5 P␣ dV = 7.5V0fpkp ignition phase and power production operation. 2 2 This criterion is only a necessary condition. It was = 1.2V0fpk(βB ) . (13) obtained under the most optimistic assumptions. Thus, ν + ν a stationary regime with an optimal plasma temperature We note that, e.g., for parabolic pressure, n T =1 f = / is assumed. The high recycling regime with a peaked in Fig. 2b, pk 4 3 (or close to 1 because of dilution temperature profile typically exhibits relaxation oscil- of DT mixture by impurities and helium). In terms of lations, and the criterion (10) should be, in fact, ex- the energy confinement time it can be written as ceeded. Also, the presence of ␣-particles and impuri- V P = . 0 . ties in the plasma reduce the peaking factor f from DT 7 5 ∗ (14) pk f τ¯ 2 its pure plasma value. Recall that radiation losses are pk E hidden in the definition of τ¯E. This form is essential to the notion of the operational In contrast to ignition, a relaxed notion of a power reactor regime. It shows that power production so-called “burning” plasma, when the criterion (10) requires a reduced effective energy confinement time τ∗ is not fulfilled, presumes a significant external power ¯E and, correspondingly, enhanced plasma pressure. for plasma heating comparable to the fusion power. Thus, for typical PDT = 3 GW for a reactor (assuming In the case of a power reactor this would conflict with 1/3 conversion into electricity and a parabolic plasma τ∗ = economics, technology and the tritium cycle. Burning pressure) the energy confinement time ¯E 1 s leads plasma would also require higher power extraction to a reasonable plasma volume V 500 m3. Energy 154 L.E. Zakharov et al. / Fusion Engineering and Design 72 (2004) 149–168

τ∗ confinement times ¯E greater than 2 s are essentially equation can be rewritten in a normalized form not suitable for the power producing phase as they dE¯ P τ¯ require a plasma volume higher than 2000 m3. τ¯ = ext − E¯ E@ign + E¯ 2 > , E@ign t f P τ 0 (18) Given the size and the power of the reactor, the en- d ␣ ␣@ign ¯E ergy confinement time for the operational power reactor E regime is determined by Eq. (13) to be typically in the E ≡ pl , p ¯ range of 0.8–1.3 s and in the range of 0.8–1 MPa. Epl@ign The relatively small energy confinement time τ¯∗ re- E E2 quired for OPRR can be comparable with the slowing pl 2 P␣ = P␣ = E¯ P␣ . (19) down time of ␣-particles [10] E2 @ign @ign pl@ign √ n 3/2 Parameters at the ignited state were used here for nor- 1 . − . 10 e n 10 . 5 4 0 3164 ln e malization. If τ¯E = τ¯E@ign independent of the heating τsd Te Te power is assumed, this equation gives the estimate for (15) the minimum necessary external power

20 −3 (ne here is in 10 m ). As a result, the pressure ph 1 1 Pext > f␣P␣@ign = f␣PDT@ign, of the hot alphas could be a noticeable fraction of the 4 20 plasma pressure . V τ > 1 5 0 . p τ τ ¯E@ign (20) h sd sd 4f␣Pext = f␣ ∗ , (16) p τ¯E τ¯ E Such a level provides the positiveness of the right f thus, reducing factor pk and efficiency of the reactor. hand side in the energy balance equation. Good confinement with an excessive energy con- Even with the small factor 1/20 in front of P , this τ DT finement time ¯E would allow for direct losses of hot expression indicates that it is impractical to ignite the f alpha particles. This would reduce the fraction ␣ and plasma at the operational point of the reactor, where p contribution of h into plasma pressure while keeping P 3–4 GW. It would require 150–200 MW of in- τ∗ DT ¯E appropriate to OPRR. stalled axillary heating power working only for a short time during the ignition phase. 2.3. Ignition phase Instead, the ignition should be performed at enhanced energy confinement time τ¯E@ign, which would τ In contrast to OPRR, the ignition parameters are be 2–2.5 times higher than the operational ¯E. Accord- determined by the available auxiliary heating power ingly, the beta value is reduced at the ignition phase. P . The power P required for igniting the plasma Ignition phase is distinct from OPRR and requires an ext ext τ is determined by the plasma energy balance equation enhanced energy confinement time ¯E@ign determined by Eq. (20) on the basis of an available auxiliary heating E E power P . d pl = P − pl + f P > . ext ext ␣ ␣ 0 (17) The power reactor should be consistent with both dt τ¯E ignition and OPRR, which have in common the same Without Pext this equation has two stationary solutions: ignition criterion but different contributions from its Epl = 0 and Epl@ignτ¯E@ign = f␣P␣@ign, where index factors. Accordingly, the transition from ignition phase ‘@ign’ refers to the ignited state. With the external to OPRR would require only a restricted, in accordance τ ∝ power present, these two solutions approach each other with√ Eq. (14), energy confinement degradation E and merge at some level of Pext, corresponding to the 1/ P␣ when the fusion power increases. minimum external power necessary for ignition. Conventional regimes contain a fundamental prob- Assuming the best possible scenario where the tem- lem in making transition from ignition to OPRR. The perature profile is kept optimal while P␣ is externally ion-temperature gradient (ITG) turbulence, associated controlled (e.g., by the density level) the energy balance with low edge temperature, preserves the core temper- L.E. Zakharov et al. / Fusion Engineering and Design 72 (2004) 149–168 155 ature gradients by enhancing energy losses and degrad- OPRR. Separation becomes bigger for larger volumes. ing the confinement [3]. The turbulence makes the tem- The dashed blue curve in Fig. 3a shows a scenario path, perature profile depend only on its edge value. starting with plasma heating by external power, then ig- In the reactor, because of the necessity an opti- nition and transition to OPRR. mal (for fusion power) level of core temperature and The ignition phase should last only several energy a low edge temperature (for power extraction in the confinement times, while the operational regime is con- diverter) its profile should be essentially unchanged tinuous and has much more challenging plasma param- during the transition. An increase in density provides eters. an increase in power. Based on this model, the ex- The high pressure plasma of OPRR (p 2 pected scaling would be P␣ ∝ n , Epl ∝ nT ∝ n, and 0.8–1 MPa) can be developed only with use of fusion −1 −1/2 τE ∝ n ∝ P , just marginal to the requirement. power as the dominant heating power. The problem is that during transition from ignition The heating power P␣ of OPRR (13), e.g., assuming to OPRR the fusion power should be raised by a factor a parabolic pressure (fpk = 4/3, p=0.8–1 MPa), of 10 and the model of "transport enhancement by turbulence" is unlikely to be applicable. At some level P␣ 1.5fpk(0.64–1)V0 (1.3–2)V0 (21) of power, “transport” most probably will be replaced 3 by bursting phenomena and then, by macroscopic re- would be too large even for a plasma volume of 50 m laxations and loss of confinement. (TFTR size). Substituting for P␣ would require 65– The consequences of an intrinsically turbulent 100 MW of external power (twice the TFTR auxiliary regime for energy confinement at power levels far power) in order to reach and sustain the OPRR. Shield- exceeding the critical level for instability are unpre- ing would lead to further enlargement of the plasma dictable. In any case, they will degrade the “expected volume and to a higher power. The available plasma marginal” scaling of τE versus power, thus, preventing heating methods simply cannot provide the power for conventional plasmas, even ignited, from transition to simulation of OPRR. OPRR. Only compact machines, like ST, with a smaller vol- V 3 The high edge temperature of the low recycling ume 0 30 m and no shielding of the central rod regimes can eliminate (or control) the ITG-turbulence, can potentially reach the OPRR level of p, and de- thus, raising expectations for both ignition and velop the regime with much less reliance on fusion OPRR. power. At the same time, as discussed later, ignition still will be required for the purpose of developing the FW 2.4. Fusion power is needed for development of design. OPRR While for large machines ignition and OPRR are separated, it may be possible to ignite an ST at the Separation of ignition and OPRR is clearly seen on relatively small energy confinement time of OPRR. P τ∗ the plot “fusion power versus energy confinement time” The ( -¯E) diagram for such an ignited ST (IST) with τ∗ τ∗ plasma volume V = 30 m3) is shown in Fig. 3b. With a ¯E in Fig. 3a. Recall that ¯E accounts for all losses including radiation and loss of ␣-particles. reasonable B = 3 T (assuming no shield on the central The black curve is the total fusion power PDT, rod) and total fusion power of about 0.5 GW, it can be P β = . . while the red one is P␣. The green line shows the ignited with ext 25–30 MW reaching 0 4–0 45 β< . level of Pext 30 MW, necessary for ignition. The at the OPRR point. For conventional plasma 0 04, dashed green line is 4Pext. Its intersection with P␣ this diagram would require a device with, at least, three determines the ignition parameters. The blue curve times higher magnetic field. gives the β-value (scale on the right side) necessary to meet the ignition criterion (11). The dashed black 2.5. Cost estimates of electricity produced curve in the low-right corner shows PDT for the ITER volume V = 834 m3. The monetary value of the electricity produced 3 For a reactor-like plasma size, V = 400 m WElectr during the life time of the reactor is limited. (Fig. 3a), the ignition phase is well separated from Assuming 30 years of uninterrupted operation, a refer- 156 L.E. Zakharov et al. / Fusion Engineering and Design 72 (2004) 149–168

τ∗ B = V = 3 Fig. 3. Fusion power vs. cumulative energy confinement time ¯E for (a) a reactor with 5 T and 400 m , and (b) for an ignited spherical tokamak with B = 3 T and V = 30 m3. ence estimate can be written as at the very early stage of development of OPRR and the FW. CkWh W [$B] = 10.5P , (22) Periodic replacement of the first wall surface (if Electr Electr 0.04 it is based on solid materials) leads to additional ex- where PElectr [GW] is the electric power of the reactor, penses for operation of the fusion reactor. The charac- e.g., PElectr PDT/3 and CkWh is the cost of 1 kWh. teristic neutron fluence for the FW life time is about The cost of the reactor should be only a fraction of 15 MW year/m2. It can be converted into the corre- 2 the monetary value of electricity produced, e.g., given sponding value CFW of electricity “produced” per 1 m by Eq. (22). during the life time of the FW element Although extremely simplified even such an estimate imposes severe restrictions on the cost of the $B 2 5.25 C C 0.001 kWh , (23) fusion reactor itself, its operation and maintenance. FW m 3 0.04 Given the $5 B cost of the 0.4 GW ITER, it suggests that the power reactor, in approximately half of where 1/3 is assumed as a conversion factor of fusion the ITER plasma volume, should have an order of power to electricity. magnitude higher fusion power. Clearly, the conven- The cost of replacement of the first wall surface tional plasma does not fit the simplest cost considera- should be within the limit CFW given by Eq. (23). tions. This requirement strongly motivates new approaches for the first wall design with emphasis on 2.6. Cost estimate of first wall replacement low activation structures and liquid elements (liquid lithium, FLiBe, Be, etc.). Correspondingly, the plasma The first wall is the most challenging structural regime should be consistent with these innovative element of a reactor, which imposes additional con- structures of the first wall. In this regard, the low re- straints on the reactor physics regime and design. The cycling regime is compatible, e.g., with the flowing necessity of using fusion power for its development lithium wall surface [11], although it requires solving ties the technology of the FW with plasma physics the problem of pumping the helium ash. L.E. Zakharov et al. / Fusion Engineering and Design 72 (2004) 149–168 157

2.7. Tritium consumption and FW development

While it is difficult to assess the total amount of tritium required for development of OPRR, the tritium consumption WT,FW for development of the first wall is straightforward to calculate, and for 15 MW year/m2 is given simply by kg W , = 1.046. (24) T FW m2 Such a large consumption of tritium automatically requires breeding tritium with efficiency close to or exceeding 100%. Three elements of magnetic fusion, i.e., OPRR, FW and tritium cycle are all linked together by the requirement of 100% tritium breeding starting from an early stage of development of a fusion reactor. Fig. 4. Neutron coverage fraction of the central pole as a function Reactor size machines are not suitable for such a of aspect ratio. (Plasma cross-section of IST in Section 6, Fig. 9 was triple-goal R&D. Thus, for accumulation of a fluence to used for calculations.) the wall of 15 MW year/m2, a configuration of the size of ITER would consume about 600–700 kg of tritium, plasma aspect ratio. Although actual losses of neutrons far exceeding any foreseeable amount of potentially depend significantly on detail and materials of the de- available non-fusion tritium (about 25 kg in the next sign, NCF is one of the primary factors, contributing three–four decades). to losses. Based on NCF, STs have significant advantage with respect to conventional aspect ratio devices 2.8. IST based component test facility is required targeting CTF requirement. The central rod in the ST for reactor R&D has a minimal averaged space angle compared to other toroidal configurations. Intrinsic link between OPRR, FW and TC, use of At the same time, the CTF, even based on an ST, fusion power and high tritium consumption create a may have an unacceptable level of neutron losses if situation when the development of the reactor requires the ports for neutral beams are not filled with tritium compact intermediate devices or a component test facil- breeding material. In order to use this reserve, plasma ity (CTF), which would be capable of accumulating the in CTF should be ignited and all NBI ports should be necessary neutron fluence and developing FW and TC. covered with the breeding material. Even in compact devices, like spherical tokamaks Note that ignition, which is motivated by tritium 3 2 (e.g., V0 30 m , FW surface SFW 55 m ), the tri- breeding considerations, is not an excessive require- tium consumption would be a big issue and full tritium ment for IST also from the plasma physics point of breeding is required. Thus, rather than being a “driven” view. In contrast to conventional plasma, STs in the device, the CTF should be a mini-reactor working at LiWall regime are not severely limited in β. The “burn- OPRR plasma parameters, almost full FW functional- ing” plasma is close to ignition anyway, and there will ity, and closed TC. The only difference from the power be no substantial plasma physics obstacles between reactor would be simplification of shielding (with some “burning” and ignition in ST. structure exposed to neutrons) and absence of elec- Among fusion configurations ignited spherical toka- tricity production. With such a simplification the CTF maks are uniquely positioned for development of could be realized in a form of IST. OPRR, FW and TC for fusion reactor. Fig. 4 shows the neutron coverage fraction, or NCF The geometry of the ignited ST together with the (surface fraction weighted using influx of primary fu- ignition regime allows the maximum use of the FW sion neutrons) of the central column as a function of surface for tritium breeding. 158 L.E. Zakharov et al. / Fusion Engineering and Design 72 (2004) 149–168

2.9. Transition from CTF to the power reactor tral particles are supplied into the core itself (either by neutral beams or by pellet injection). On the way to the reactor, first, the OPRR plasma With the boundary localized particle source, the par- regime should be developed (probably with limited ticle confinement time near the edge is small, leading or no breeding of tritium). While the plasma pressure to intense mixing of plasma particles at the edge. As of OPRR can be potentially achieved in two types a result, the edge plasma temperature is relatively low of compact machines: IST or high-field conventional compared to its core value. The temperature profile is tokamaks, only ISTs are consistent with the following peaked, while the density profile is flattened. development of FW and TC. In the second case with core fueling, the particle The way to fusion power reactor includes, first, confinement time corresponds to the core confinement. achieving OPRR plasma parameters on LiWall IST, If the plasma is well pumped from the edge, the wall second, a phase of development of FW and TC on and its temperature are not “visible” to the plasma. As IST based CTF, and then transition to the reactor a result, a high plasma edge temperature, comparable itself. with its core value is established when the plasma par- Thus, the IST and its CTF phase should bear the ticles are gradually heated while diffusing through the major part of practical fusion development. Essentially, core toward the boundary. The temperature profile be- ISTs could demonstrate all three objectives of magnetic comes flattened or hollow, while the density profile is fusion and would represent the most crucial step toward peaked in accordance with the position of the particle the fusion reactor. Then the transition to a power reactor source. will require changing the plasma geometry (to conven- Both situations are described by the following tional aspect ratio), developing the full functionality of boundary condition for the energy transport equation the FW (including high grade heat extraction from the blanket), and full shielding of the neutron zone. Other γΓ micro T = P V, edge→wall edge heat d (25) changes (e.g., superconducting coils, heat conversion into electricity, etc.), are supplementary to these reactor written for each species of the plasma (convection core transformation. coefficient γ = 5/2 for Maxwellian plasma). Here, Improvements of the present plasma parameters, its Γ micro is the particle (microscopic) flux toward the stability and confinement would require, first of all, edge→wall wall, T is the edge temperature, P is the density making a transition to the high edge plasma tempera- edge heat of heat source, dV is the plasma volume element. ture and solving associated plasma boundary problems. In the high recycling case the plasma particles are Lithium covered stabilizing walls (e.g., copper with ei- resupplied to the edge after collisions with the wall ther solid, molten or liquid Li surface and a special surface. In this case, Γ micro , which is the directed interface layer) positioned right at the plasma bound- edge→wall plasma particle flux to the wall, is much large than the ary and complemented with the power extraction sys- particle diffusion (macroscopic) flux inside the plasma. tem suggest a practical approach for developing the IST As a result, the edge temperature is low compared to grade plasma. At the R&D stage the physics of the new the core temperature regime does not require intense lithium flows. Γ micro Γ , edge→wall core 3. Basics of plasma confinement in the 1 T P dV Tcore. (26) edge γΓ micro heat low-recycling regime edge→wall

With respect to the boundary conditions and to This formula is approximate to the extent that the en- plasma fueling two kinds of plasma regimes can be ergy of the particles in the edge localized source was distinguished in quasi-stationary configurations: high- neglected with respect to the core temperature. Also, and low-recycling. In the first one, the plasma is refu- due to possible non-Maxwellian distributions the γ co- eled by neutral gas through the boundary, while in the efficient in the convective energy flux can be different second, the boundary is pumped out, while the neu- from 5/2. L.E. Zakharov et al. / Fusion Engineering and Design 72 (2004) 149–168 159

particle diffusion, qχ 5/2 ΓT . Thermo-conduction tends to make the profile flat and, thus, returns some energy from the boundary into the core. Inside the localized source, the situation is the same as in the conventional regime, where the plasma density is flattened, the convective losses are small and the energy transport is dominated by thermo-conduction, qχ 5/2 ΓT . A peaked temperature profile is established in this region, referred to here as χ-region. The D-region is the key feature of the low recycling regime, having different and, potentially much Fig. 5. χ- and D-confinement regions in the low recycling regime. (a) Electron and ion temperatures for three values of thermo-conduction improved, confinement properties than the conven- coefficients, related to each other as χ2 = 2χ1, χ3 = 10χ1 (index is tional plasma. First, because of ambipolarity, the en- the curve number on the plot), and same particle diffusion. (b) Elec- ergy losses in the D-region are determined by the best tron, ion (deuterium) density and localization of the particle source. confined plasma component and are less sensitive to thermo-conduction than in the χ-region. A comparison In the low recycling case all particles are absorbed of cases with 3 values of thermo-conduction coefficient by the wall and “microscopic” flux is equal to “macro- in Fig. 5a shows that the only effect of significantly (10 scopic” one times) enhanced thermo-conduction is a small change Γ micro Γ , in the temperature profile. edge→wall core Experimentally, there are indications that reduced 1 recycling leads to improved confinement. Thus, all Tedge = Pheat dV Tcore. (27) γΓcore TFTR high performance regimes were achieved with “lithium conditioning”, resulting in reduced recycling The plasma energy, essentially, is not affected by the [12] (although explained within conventional ITG wall and the edge temperature reaches its natural level, theory [13]). The most prominent results with high comparable or exceeding the core temperature. Instead, plasma temperature and enhanced edge pumping have the density at the edge becomes very low (thus, elim- been obtained on DIII-D in a quiescent double barrier inating the Greenwald density limit [7]). In the low regime [14], demonstrating good confinement and a recycling case, it is possible to expect a less turbulent stable plasma. (or stabilized at high beta of IST) plasma, where the Theoretically, the presence of the D-region creates γ / rate of convection is described by a factor 5 2. a special situation for the confinement, not studied yet Two confinement regions are present in the plasma in the tokamak research. Although there are no theory for the case of core fueling and pumping walls, as simulations of turbulent transport in the low-recycling is shown in Fig. 5. With respect to the position of regime, which would give a corresponding transport the core particle source, there are different contribu- model, theory unambiguously concludes that an tions from convective (or particle diffusion term) and increase in the edge temperature improves the core q thermo-conduction χ energy transport into the total confinement [2]. Q energy flux As an example, ASTRA code calculations of low re- 5 V cycling plasma performance using the PPPL-IFS trans- Q = ΓT + qχ = Pheat dV. (28) port model [15,16] for ITER-FEATtokamak are shown 2 0 in Fig. 6 with boundary conditions (27) and γ = 3. The Outside the localized particle source, the temperature core fueling was simulated by a particle source Sn local- profile relaxes to its natural level, when the particles ized at 0.5 m from the plasma edge (Fig. 6a). A substan- acquire energy from the heating source, while diffusing tial temperature pedestal, Ti(a) 10 keV, develops at toward the wall. As a result, the temperature profile is the edge, and the entire plasma cross-section produces hollow in this region, referred to here as the D-region. the fusion power. The ITER plasma would be ignited The energy losses here are determined solely by the (Fig. 6b) if such a low recycling regime could be es- 160 L.E. Zakharov et al. / Fusion Engineering and Design 72 (2004) 149–168 tablished. In simulations, the low recycling regime has prevents better confinement despite elimination of the been “started” at some time from a stationary standard thermo-conduction energy loss. At the same time, for ITER plasma. After establishing a high edge tempera- the low recycling regime there is no real justification ture at t = t0, its fusion power increases in calculations for such a ∝ 1/ne diffusion model, which originated (Fig. 6b), tripling the reference value of 400 MW. from the global energy (not the particle) confinement The expected enhanced confinement in the low scaling obtained for much higher plasma density. recycling plasma, its presumably, smaller sensitivity Control of the temperature pedestal in the low recy- to turbulence and to the heating power [12] could cling plasma regime would give an unambiguous test of make the LiWall regime suitable for the OPPR and existing thermo-conduction models as well as unique its development path. Moreover, as it is shown later, information on the diffusion properties of the plasma. in spherical tokamaks the residual micro-instabilities, i.e. electron trapped modes, can be stabilized in the D-region at sufficiently high plasma beta. This would 4. Particle and power extraction by close-fitting lead, potentially, to neo-classical confinement and LiWalls open the possibility for reaching even D3He (or 3He “catalyzed DD”) fusion. Exceptional properties of pumping hydrogen Note, that in the ITER-FEAT example of Fig. 6, the plasma particles by lithium have been observed in toka- high fusion performance was solely a result of the in- maks during the very first experiments involving a large creased volume of plasma participating in fusion. The area of lithium coated wall surface on T-11 [17–20] and diffusion model used in simulation includes ∝ 1/ne with rail [21] and toroidal liquid lithium limiter [22,23] diffusion coefficient, leading to a sharp drop of den- on CDX-U spherical tokamak. sity near the edge, enhanced particle flux in the D- An assessment of the pumping capacity of the region and energy loss. Such a diffusion model, in fact, lithium surface can be made using a rather realistic

Fig. 6. (a) Plasma radial profiles: core localized particle source S, electron ne density, electron Te and ion Ti temperatures, and q profiles as functions of the minor radius. (b) Time evolution of central Ti(0) and edge Ti(a) ion temperatures, fusion power PDT and the particle flux to the wall Γw. L.E. Zakharov et al. / Fusion Engineering and Design 72 (2004) 149–168 161 assumption that Li can absorb the hydrogen atoms tially establishes the evaporation limit at approximately essentially at the ratio 1/1 with respect to the Li atoms. 400◦. Also, it makes the plasma sensitive to potential According to TRIM code calculations (J.P. Allain, “hot” spots at the wall. University of Illinois), in solid lithium about 150–200 At the same time, evaporation does have an effect mono-layers of Li (for energy of the hydrogen atoms on the particle flux to the wall, and, thus, on the edge of 2 keV) can work for pumping. In liquid or molten plasma temperature, as was explained in the previous Li, macroscopic depths are involved due to thermal section, Eq. (26). In this regard, strong dependence of CLi diffusion. Accordingly the pumping capacities pump Li evaporation on the wall surface temperature sug- for these two cases are characterized by gests a straightforward way to control the confinement regime by affecting evaporation and the edge plasma 1020 Csolid Li 27 , temperature. pump 1m2 Sputtering, as another source of contamination by 1020 Li, cannot contribute significantly into contamination Cmolten Li 46,000 . (29) pump 1m2 × 0.1mm because it corresponds to the edge Li source, which is only a fraction of the core source of plasma parti- Relatively small amounts of either solid or molten cles. Also, at plasma temperatures higher than 500 eV, Li (utilizing thermal mixing of the particles inside sputtering is degraded with plasma temperature. the layer) on the wall surface are required for plasma Regarding Li edge source control, a copper shell is pumping. For 1 h of continuous operation of the ITER an excellent material behind the lithium layer, which sized plasma, for example, only2Lofmolten lithium can provide (even with no active cooling) an exposure (or 20 m2 of the surface coverage by 0.1 mm thick time given approximately by molten lithium) would be necessary.  *T 2 *T The pumping capacities of a lithium surface far  wall wall 2 d2 π if < , exceed what is necessary for absorbing the plasma T1 T1 π texposure (31) particle flux, thus allowing different arrangements for 4D  *T 4 *T 2 4 wall − if wall > , the LiWalls, including coating (micron thin solid Li), T1 π T1 π “painting” (tens of microns molten Li), gravity or elec- where, d is the thickness of the wall, q is the energy tromagnetically driven boundary layer flow (fraction of wall flux to its surface, *T is the allowable temperature mm liquid Li with velocity in the range of cm/s) or elec- wall increase, and T and D are defined as tromagnetically propelled liquid lithium flow (fraction 1 q κ of cm thick layer with about 10–20 m/s speed). T ≡ d wall ,D≡ T , 1 κ ρc (32) The power extraction requirement is that the heat T p load to the lithium surface should be distributed in order κ ,ρ,cp ◦ with T being the thermoconduction coefficient, to prevent heating the free Li surface to above 400 C. mass density and specific heat of the wall, respectively. Γ Near this temperature the evaporation rate Li of Li can The combination of lithium layer and copper wall be approximated as (κT 393,ρ= 8960,cp = 400 in SI units) would al- 2 ◦ q / T −400 C low a reactor relevant heat flux wall 2MW m (an 20 ◦ 1 ΓLi 3 × 10 e 50 C (30) order of magnitude larger than, e.g., in ITER) for 10– m2 s ◦ 30 s (d 5 cm, *Twall 400 C) with a stabilizing and is comparable with expected particle flux from the highly conducting shell right at the plasma boundary. − reactor 2–3×1020 (m2 s) 1. Note, that comparable or Li and copper is a unique combination suitable for de- even modestly exceeding surface source of Li (with velopment of the plasma physics aspects of OPRR. small particle confinement time) cannot compete with Flowing lithium requires high velocities in order to the core fueling of the plasma and, thus, contaminate withstand the reactor relevant power fluxes to the wall the plasma. (This contrasts with the conventional situa- ◦ qwall tion when both plasma particle and impurities have the *TLi = 200 C 4texposure, 3.5MW/m2 edge localized source.) Nevertheless, the exponential dependence of evaporation on wall temperature essen- dskin (mm) = 4.8 4texposure, (33) 162 L.E. Zakharov et al. / Fusion Engineering and Design 72 (2004) 149–168 where dskin is the thickness of the heat absorbing 2 surface layer. For qwall 3.5 MW/m it gives 1/4 s of exposure time, corresponding to a velocity V 20 m/s and the working layer dskin 5 mm. Intense lithium streams, driven by magnetic propulsion have the necessary properties [11] and should be developed for such a case. All the options listed above for reactor relevant heat fluxes require a lithium surface well aligned with the plasma. At smaller heat flux, as well as at lower beta (when the conducting shell is not required), other pos- sibilities may exist. Even a diverter plasma, according to experiments, is interacting with the wall due to so- called “blob” transport mechanism [24,25]. This would suggest effective pumping of the plasma by the Li wall surface even in a diverter configuration.

5. Stability of LiWall limited plasma Fig. 7. Stability diagram for fixed boundary plasma with a current density pedestal. (Calculated using ESC, DCON, PEST and BAL- A flattened temperature profile, beneficial for en- LOON stability codes for n = 1, 2, 3, ∞ MHD modes.) ergy confinement, results in a flattened current density profile j with a current pedestal at the plasma edge, with the same aspect ratio and for two different values jedge = 0. Also, at high betas, which are necessary for of central q. First, there is a dramatic enhancement OPRR, the bootstrap current makes a significant con- of stability β-limits, compared with the conventional tribution to the plasma current density. The bootstrap plasma when the current density pedestal becomes current jBS, which is proportional to the plasma pres- comparable with the central current density. Second, sure gradient, jBS ∝ p , also leads to the current density the plasma shape becomes less important for stability pedestal at the edge. in the low recycling regime. For both circular and With the plasma boundary separated from the con- non-circular configurations, nearly flat current density ducting wall, the current edge density pedestal further profiles have β-limits higher than required for OPRR. reduces the stability of conventional plasma regimes. Conventional plasmas with peaked temperature and The suggested so-called “profile control” for tailoring the current density profile, even with hypothetical sta- the current density distribution in order to improve bilization of free boundary modes by some plasma stability remains speculative for reactor power levels. physics mechanisms (e.g., by plasma rotation), would LiWalls can change the stability situation in toka- remain entrapped in the “first stability” regime, insuf- maks in a crucial manner by allowing for a conducting ficient for OPRR. wall positioned right at the plasma boundary and, po- Fig. 8 illustrates the difference in stability proper- tentially, for eliminating the free boundary instabilities. ties of peaked and flat current density profiles with the This allows utilization of the high beta of the second fixed plasma boundary. The first two configurations stability regime resulting from a flattened (or reversed) (marginally unstable) have a peaked current profile. current density profile. Thus, the properties of LiWalls Their pressure gradient is limited in both the center and justify a new parameter in stability optimization, i.e., at the edge, thus, requiring “profile control” for stability the current density pedestal in conjunction with the optimization. The third configuration has a flat current fixed boundary plasma, as shown in Fig. 7. density, much higher beta limits and is less sensitive to The blue curve in Fig. 7 indicates the β stability the pressure profile. limit for TFTR-like circular tokamak geometry, while It is a unique property of LiWall regimes that flat- two black curves are β-limits for elongated plasma tened temperature and current together with pumping L.E. Zakharov et al. / Fusion Engineering and Design 72 (2004) 149–168 163

Fig. 8. Magnetic configurations and plasma profiles for “first” and “second” stability regimes. (a) Core ballooning unstable β = 4.6% configuration with a peaked pressure profile. Pink color shows ballooning instable region. (b) Edge ballooning unstable β = 5.3% configuration with a flattened pressure profile. (c) Second stability with β = 16%. (d) Current density profile j(a), black for configurations (a, b) and blue for configuration (c). (e) Corresponding q(a)-profiles. (f) Pressure profiles p(a), black for configurations (a, b) and blue for (c). For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article. and a stabilizing wall are consistent with each other. tional reasons why STs are unique for developing the The expected enhanced confinement and β limits may magnetic fusion were revealed. satisfy two of the most important requirements of the The value of the magnetic field is rather restricted reactor OPRR. In addition, in the LiWall environment in spherical tokamaks by limitations in space for the the bootstrap current, enhanced by high-β, does not re- central rod of the toroidal magnetic coils. In the case duce the ideal plasma stability as it would happen with of ignition, there is no possibility of using supercon- conventional free boundary plasma. ductivity for toroidal coils. Also, it is problematic to rely on the central solenoid for current excitation in an ignited ST. 6. Ignited spherical tokamaks The low recycling regime and stabilization of the free boundary instabilities by LiWalls open a wide pa- Spherical tokamaks are the leaders in achieving the rameter space for ignited operation with OPRR plasma highest β 0.35 values at a good, tokamak range, en- parameters and self-sufficient bootstrap current. Here, ergy confinement time [26]. Earlier in the paper addi- we show that the high β limit in low recycling STs 164 L.E. Zakharov et al. / Fusion Engineering and Design 72 (2004) 149–168 compensates for the relatively low value of the mag- is technically feasible and would be sufficient for netic field and makes an ignited ST feasible. robust plasma stabilization at β 0.4–0.45 with the Concerning the bootstrap current, high β and sec- pressure exceeding the OPRR level of 1 MPA. A flat ond stability make two situations possible, (a) when parallel current density j is assumed for the current plasma is overdriven with the bootstrap current, and distribution together with the simplest model of the (b) when the configuration is essentially maintained by pressure distribution dp/d1 = const. In contrast to the bootstrap current. Thus, ignition can be initiated at the conventional plasma, an IST with a finite current the lower plasma current and then, the configuration density at the edge and wall stabilization does not will slowly evolve to the stationary state due to only require pressure profile tailoring. bootstrap current drive. Such an IST configuration would have fusion power PDT = 658 MW (with Prad = 36.5MW at Zeff 1) 6.1. Ignition conditions for IST τ∗ = . and would require only ¯E 0 49 s (or, with radiation τ∗ = . subtracted, E 0 68 s) energy confinement time. In the following examples, the low recycling regime Its total current I = 8.5 MA should be initiated by T a = T a = pl was simulated by a flat temperature e( ) i( ) inductive current drive, while after ignition it will be a 15 keV, where is radial coordinate related to the maintained and, in fact, enhanced by the bootstrap toroidal magnetic flux Φ current drive. Φ The IST configuration has other properties consis- a ≡ tent with the requirements for development of the FW Φ (34) 0 and TC. Thus, with only 10% neutron loss in the central rod (52 MW of the power in neutrons), the average (Φ0 is the total toroidal flux in the plasma). A particular neutron load on the outer wall is 10.7 MW/m2, which configuration with the inner Ri = 0.5 m and outer Re = 2.0 m radii and the plasma height 3 m is considered. exceeds by an order of magnitude projections based on The entire plasma of such an ST would fit into the conventional plasma regimes. ITER-FEAT plasma cross-section. The plasma volume V = 26 m3 and the surface S = 53.4m2 are about 30 6.2. Self-sufficiency of bootstrap current and 12 times smaller than the corresponding plasma volume and surface of ITER-FEAT. In consideration of a stationary plasma with low The value of the toroidal magnetic field Btor = 7.5T edge temperature there is always a conflict between sta- at R = Ri and 3 T at the plasma geometric center bility of free boundary MHD modes and high value of

Fig. 9. (a) Stable magnetic configuration of ignited spherical tokamak with Ipl = 8.5 MA, β = 0.46. (b) Parallel current density and q-profile. (c) Pressure profile (exceeding OPRR level). L.E. Zakharov et al. / Fusion Engineering and Design 72 (2004) 149–168 165

tion of the bootstrap current based on direct particle orbit simulations. The blue curves (dashed and solid) in Fig. 10 represent the bootstrap current calculated with Maxwellian and mono-energetic particle distribution functions. The red and brown curves are contributions from ions and electrons. The standard theory, developed for conventional aspect ratio [27] gives 25% higher value than the particle simulations. The black dotted curve represents the col- lisionless theory model and black dashed curve results from the theory with collisions at T = 15 keV. (At this moment, the reason of some discrepancy between theory and particle simulation results is not yet understood.) The solid black line in Fig. 10 represents the parallel current distribution in the configuration. Both particle orbit simulation and the theory indicate a significant value of the bootstrap current over j everywhere except in the plasma center. Fig. 10. Bootstrap current profile in IST configuration of Fig. 9. Bootstrap current overdrive does not represent a problem for the IST. The IST provides a wide oper- the bootstrap current. For optimization it would require ational space for variations of plasma current density the so-called “profile control”. In contrast, with a flat and pressure, even at a level exceeding OPRR require- Ti,e const. = 15 the LiWall stabilized IST configu- ments. In particular, a stationary configuration with al- rations can be overdriven by bootstrap current without most 100% alignment of the bootstrap current with the violating stability. plasma current is achievable with no deterioration of The bootstrap current calculations for the IST con- stability or the fusion power. figuration of Fig. 9 are shown in Fig. 10. The OR- Fig. 11 shows an example of a configuration, with BIT code (R. White) has been used for calcula- a pressure profile similar to the previous case and the

Fig. 11. (a) Stable magnetic configuration of bootstrap current maintained IST configuration with Ipl = 9.2 MA, β = 0.44. (b) Parallel current density j (blue) aligned with the bootstrap current (red) and q-profile. (c) Pressure profile. For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article. 166 L.E. Zakharov et al. / Fusion Engineering and Design 72 (2004) 149–168 current profile aligned with the bootstrap current ev- zone could be, if necessary, compensated by other kinds erywhere, except for a small region near the mag- of current drive. netic axis. Here, the bootstrap current has been calculated using orbit particle calculations as a normaliza- 6.3. Magnetic well, suppression of tion for theory formulas. This configuration has a fusion micro-instability power PDT = 649 MW (Prad = 36 MW) and requires the same energy confinement time for ignited operation An exceptional property of the IST configuration is τ∗ = . τ∗ = . (¯E 0 49 s, E 0 68 s). that it has an absolute magnetic well inside the plasma. Note that the center region is the most favorable Fig. 12 shows the amplitude of the total magnetic field for the radio-frequency current drive methods because |B|, calculated along the θ =const-lines in the radial of the reduced fraction of trapped electrons. Thus, the direction (θ is the poloidal angle in the cross-section). deficiency in the bootstrap current in the small central In the plot n is the toroidal wave number of the mode,

Fig. 12. (a) Stable magnetic conﬁguration of Fig. 9 (IST with Ipl = 8.5 MA, β = 0.46). Red lines correspond to θ = const. (b) |B| as a function of a for 64 equidistant θ values. (c) |B| as a function of a for 5 θ values near the outer middle plane. For interpretation of the references to color in this ﬁgure legend, the reader is referred to the web version of this article.

Fig. 13. (a) Growth rate of ETM at a = 0.6 as a function of electron βe(0). (b) Growth rate of n = 5 ETM mode (most unstable) as a function of a at βe(0) = 0.7, corresponding to ITS parameters of Fig. 9. Solid curves corresponds neglecting collisions, dotted curves are calculated with collisions at T = 15 keV. L.E. Zakharov et al. / Fusion Engineering and Design 72 (2004) 149–168 167

γ, ωA0 are the growth rate and Alfven frequency, cor- lated to the solid wall environment (discussed else- respondingly. where [34]), make the conventional plasma incon- Fig. 12c shows that an absolute minimum of |B| sistent with the high power density of the power exists inside the plasma between the magnetic axis and reactor. the outer edge. The field gradient at the outer board of Another kind of plasma is required to achieve the IST reaches a value key objectives of magnetic fusion, i.e., development of OPRR, first wall and tritium cycle. The concept, dis- |B| d −1, cussed in this paper, suggests the LiWall regime suit- |B| R 2m (35) d θ=0 able to both OPRR and to its development path. The LiWall regime is also consistent with new technology which is much larger than the curvature of the magnetic approaches (e.g., liquid lithium walls) required for first field lines 1/R. In this situation, the plasma particle wall development. precession reverses its direction and puts electrons out Ignited spherical tokamaks, or ISTs, suggested in of resonance with diamagnetic frequency. As a result, the paper as an implementation of the LiWall concept, the trapped particle instabilities can be stabilized [28– could be practical devices for developing elements 31], thus, removing the residual turbulence from the of the power reactor, including ignition, obtaining D-region of low recycling plasma. parameters of the operational regime, designing the Fig. 13 shows such a stabilization of electron trapped first wall and starting the tritium cycle technology. modes (ETM) by enhanced beta in IST configuration, Basic theoretical limits for stable β and bootstrap calculated using the HINST code [32]. current, being very restrictive for the conventional Increase in β stabilizes modes as is shown in plasma, provide a wide parameter space for stationary Fig. 13a. All modes with n>5 become stabilized in- ignited operation of IST with the wall-stabilized dependent of the effect of collisions (stabilizing). At plasma and with a flattened temperature. The real the full plasma pressure, even the n = 5 mode is com- question is to what extent these opportunities can be pletely stable at a>0.6. materialized. Thus, at high β of IST, the electron trapped modes While potentially eliminating or, at least, down- can be stabilized by reversed particle precession. In this grading numerous problems related to plasma physics case, with no micro-turbulence present in the D-region (ITG turbulence, sawtooth oscillations, free-boundary of the low recycling plasma, the configuration can, modes, impurities, Troyon β-limits, etc.) and to tech- potentially, approach the condition of D3He fusion, nology (localized power deposition, activation, diffi- (requiring higher plasma temperature and about 25–50 culties with plasma stability control and use of FLiBe, times, depending on dilution by ␣-particles, better etc.) the LiWall concept depends crucially on solv- confinement [33]). At the same time, our consideration ing several issues. Some of them are common with of the OPRR, which requires a high power density, the conventional plasma while others are specific suggests that for power production the D3He (or other to LiWalls. “advanced” fuel) fusion is impractical. The outstanding problem is the feasibility of core fueling. It determines the extent of the D-region in the outer plasma core and, thus, the degree of 7. Summary confinement improvement over the conventional plasma. In fact, core fueling is required anyway (e.g., As an approach to a fusion reactor the conven- for tritium fueling) even in the conventional reactor tional tokamak plasma has insufficient performance. considerations. The second problem, specific for Limited by degradation of confinement at increased LiWalls, is electron behavior at the Li surface. Thus, power and by low stable β, such a plasma can reach, any excessive secondary electron emission from the at the best, only “burning” or ignition conditions. Fun- wall into the plasma would cool down the plasma damental plasma physics limitations prevent the con- electrons, thus, preventing the high temperature edge. ventional plasma from achieving the operational power The third problem is the helium ash pumping, which reactor regime. In addition, technology aspects re- would probably require a different solution at the 168 L.E. Zakharov et al. / Fusion Engineering and Design 72 (2004) 149–168 stage of IST and in the reactor. LiWalls and ISTs open [9] D.L. Book, NRL Publication 177-4405, NRL, Washington, DC, also an unexplored area of tokamak stability research 1990, p. 57. associated with a deep core second stability regime [10] D.L. Book, NRL Publication 177-4405, NRL, Washington, 1990, p. 31. and wall limited high temperature plasmas. [11] L.E. Zakharov, Phys. Rev. Lett. 90 (2003) 045001. Despite the existence of a number of concep- [12] D.K. Mansfield, et al., Nucl. Fusion 41 (2001) 1823. tual problems, the low recycling plasma is more ad- [13] D.A. Ernst, et al., Nucl. Fusion 38 (1998) 13. vanced than the conventional one essentially in all re- [14] C.M. Greenfield, et al., Plasma Phys. Contr. Fusion 44 (2002) actor relevant aspects. Its comprehensive study would 123. [15] W.Dorland,M. Kotschenreuther, M.A. Beer, G.W.Hammett, in: open new opportunities for both plasma physics and Proceedings of the 15th International Conference on Plasma technology of the fusion reactor. By significantly Physics and Controlled Nuclear Fusion Research, vol. 3, extending the scope of plasma regimes, the high Seville, 1994, International Atomic Energy Agency, Vienna, edge temperature plasma can also uniquely contribute 1995, p. 463. to the fundamental physics of plasma stability and [16] M. Kotschenreuther, W. Dorland, M.A. Beer, G.W. Hammett, Phys. Plasmas 2 (1995) 2381. confinement. [17] V.B.Lazarev, A.G. Alekseev, A.M. Belov, S.V.Mirnov, Plasma Phys. Rep. 28 (2002) 802. [18] V.B.Lazarev, et al., in: Proceedings of the 26th EPS Conference Acknowledgments on Controlled Fusion and Plasma Physics, vol. 23J, Maastricht, June 14–18, ECA, Geneva, 1999, p. 845. [19] V. Evtikhin, et al., in: Proceedings of the 18th Interna- This work was supported by United States De- tional Conference on Plasma Physics and Controlled Nu- partment of Energy contracts nos. DE-AC02-76-CHO- clear Fusion Research, vol. EXP4, Sorrento, Italy, Interna- 3073. tional Atomic Energy Agency, 2000, p. 21. http://www.iaea.or. at/programmes/ripc/physics/fec2000/html/fec2000.htm. [20] V. Evtikhin, et al., Fusion Eng. Des. 56–57 (2001) 363. [21] G.Y. Antar, et al., Fusion Eng. Des. 60 (2002) 157. References [22] R. Kaita, et al., Fusion Eng. Des. 61–62 (2002) 217. [23] R. Majeski, et al., J. Nucl. Mater. 313–316 (2003) 625. [1] R. Aymar, V. Chuyanov, M. Huguet, Y. Shimomura, Nucl. Fu- [24] M.V.Umansky, S.I. Krasheninnikov, B. LaBombard, J.L. Terry, sion 41 (2001) 1301. Phys. Plasmas 5 (1998) 3373. [2] A.M. Dimits, et al., Phys. Plasmas 7 (2000) 969. [25] M.V. Umansky, et al., Phys. Plasmas 6 (1999) 2791. [3] ITER Physics Expert Group on Confinement and Transport, [26] D.A. Gates, Phys. Plasmas 10 (2003) 1659. ITER Physics Expert Group on Confinement Modelling and [27] S.P. Hirshman, Phys. Fluids 31 (1988) 3150. Database and ITER Physics Basis Editors, Nucl. Fusion 39 [28] M. Rosenbluth, M.S. Sloan, Phys. Fluids 14 (1971) 1725. (1999) 2175. [29] C. Bourdelle, et al., Phys. Plasmas 10 (2003) 2881. [4] F. Troyon, et al., Plasma Phys. Contr. Fusion 26 (1984) 209. [30] J.C. Adam, W.M. Tang, P.H.Rutherford, Phys. Fluids 19 (1976) [5] Y. Shimomura, et al., Nucl. Fusion 41 (2001) 309. 561. [6] F. Porcelli, D. Boucher, M.N. Rosenbluth, Plasma Phys. Contr. [31] W.M. Tang, G. Rewoldt, L. Chen, Phys. Fluids B B29 (1986) Fusion 38 (1996) 2163. 3715. [7] M. Greenwald, et al., Nucl. Fusion 28 (1988) 2199. [32] N.N. Gorelenkov, et al., Phys. Plasmas 3 (1996) 3379. [8] G.H. Miley, H. Towner, N. Ivich, AEC Report COO-2218-17, [33] W.M. Nevins, J. Fusion Energy 17 (1998) 25. NE Program, Univ. of Illinois, 1974. [34] M.A. Abdou, et al., Fusion Eng. Des. 54 (2001) 181.