RECENT RESULTS FROM ZAP ENERGY’S SHEARED-FLOW-STABILIZED Z PINCH EXPERIMENTAL PLATFORMS

Summary

This paper presents recent experimental results from Zap Energy’s sheared-flow-stabilized (SFS) Z-pinch platforms, FuZE and the megaJoule-class FuZE-Q. Multi-point Thomson scattering measurements confirm core electron temperatures exceeding 2 keV simultaneous with sustained thermonuclear neutron emission, following an adiabatic current scaling of I^11. Modeling and power-balance analyses further demonstrate the robustness of the SFS Z-pinch concept to impurity contamination and explore conditions for achieving high scientific gain (Qsci ≥ 10).

Authors and Abstract

RECENT RESULTS FROM ZAP ENERGY’S SHEARED-FLOW-STABILIZED Z PINCH EXPERIMENTAL PLATFORMS B. LEVITT, D. A. SUTHERLAND, E. T. MEIER, J. R. BARHYDT, C. LIEKHUS-SCHMALTZ, U. SHUMLAK Zap Energy, Seattle, USA. Email: [email protected] G. A. WURDEN Los Alamos National Laboratory, Los Alamos, NM C. GOYON, A. E. YOUMANS, D. P. HIGGINSON Lawrence Livermore National Laboratory, Livermore, CA S. C. BOTT-SUZUKI, J. T. BANASEK University of California San Diego, La Jolla, CA

Abstract Sustained fusion reactions have been measured in a Te, Ti > 2 keV deuterium Z-pinch plasma which is stabilized by radially sheared axial flows. Thomson scattering results from the FuZE device [1, 2] show the onset of high plasma temperature is coincident with a stabilized quiescent period and neutron production. Measurements from neutron detectors demonstrated that 2.45 MeV neutrons were emitted from an extended portion of the 50-cm pinch assembly region, the length of which can be controlled by the specifics of the deuterium gas injection [3]. Additionally, neutron spectroscopic measurements indicate a thermonuclear production process with limited beam-target effects [4]. A new experimental platform, FuZE–Q[5, 6], is now online, and for the first time couples a SFS Z pinch to a megaJoule class capacitor power bank, extending the operational regime and plasma performance of these devices. The neutron yield scaling from recent FuZE-Q campaigns shows strong dependence on pinch current in both model and experiment, agreeing with a simple scaling model consistent with ∝ I^11 [7, 6]. These promising results indicate that a sheared-flow-stabilized (SFS) Z pinch could scale to an extremely compact, economical fusion power plant. Investigations of the effect of plasma wall interactions show that the SFS Z pinch concept may be relatively robust to the effects of impurity contamination, with specific design points capable of accessing Qsci ≥ 10 with Zeff ≈ 4. This is a significant finding for this configuration, which features direct contact of the high β fusion-generating plasma with plasma facing material surfaces.

1. INTRODUCTION

In a static Z-pinch equilibrium, an axial pinch current radially confines plasma pressure such that increasing the current results in higher densities and temperatures. While virulent pressure-driven instabilities are known to quickly destroy the traditional Z-pinch equilibrium, theory showed that introducing a sheared axial flow stabilizes the plasma [8]. Closely coupled with computational studies, a series of Z-pinch experiments at the University of Washington [8, 9, 10, 11] tested the theory of sheared-flow stabilization, showing the effect of velocity shear on instability growth, as seen qualitatively in Fig. 1. Experimental measurements of the plasma equilibrium and stability confirmed that in the presence of a sufficiently large flow-shear, gross Z-pinch instabilities were mitigated, and radial force balance was achieved [7]. Both the image from the V-UV fast camera and the modeled ion density profile in Fig. 1 show similar structures, which are indicative of sheared instability structures associated with delayed mode growth and limitations to radial fuel losses. In various generations of SFS Z-pinch plasmas, discharges of 50, 100, and 126–cm lengths were held stable for durations much longer than predicted for a static plasma, i.e. thousands of mode growth times [7].

This paper summarizes recent studies on two SFS Z-pinch devices at Zap Energy: the FuZE and FuZE-Q platforms. FuZE was built and operated at the University of Washington before moving to a Zap Energy facility in 2020, while FuZE-Q was designed, built, commissioned and is currently operated fully by Zap Energy staff. The two devices are fully operational, each with separate capacitor power banks and a complete plasma measurement diagnostic suite for science evaluation. The FuZE device is driven by a lower stored energy bank, ∼80 kJ, and focuses on core science studies, device concept development, and diagnostic testing, while FuZE-Q has a much larger current driver, ∼1 MJ, for fusion performance optimization. Updates on selected recent results from both devices are covered in this paper along with a look forward to assess the robustness of the SFS Z-pinch concept to impurity content for future power plant relevant scenarios. Section 2 covers recent experimental results, beginning with a description of our diagnostic capabilities; presenting Thomson Scattering and soft xuv measurements of Te from the FuZE device; and covering descriptions of the pinch axial extent, as measured by V-UV fast cameras as well as an axial arrays of neutron detectors. Section 3 briefly describes performance scaling SFS Z pinches to relevant gain scenarios via adiabatic compression and presents supporting results from both devices. Section 4 further outlines how performance scaling may be effected by inclusion of impurity content, which is a key risk for this concept. Finally, we conclude in Sec. 5.

2. RECENT PROGRESS

2.1. FuZE-Q Diagnostic Suite Based on these early studies and the strong indications of performance scaling, Zap Energy is developing the SFS Z pinch for fusion energy applications. The efforts to achieve the necessary performance improvements are aided by a suite of advanced diagnostics, summarized in Fig. 2: an array of 94 in-vacuum surface magnetic probes spaced axially and azimuthally are embedded into the outer electrode to measure the field and current distribution of the plasma at the wall; a suite of fast plastic scintillating detectors, or SPMTs, (labeled “n” in the figure) measure the temporal and spatial neutron source as well as neutron energy spectroscopy [3, 4]; a series of neutron activation detectors (Lanthanum Bromide, Arsenic, Rhodium) measure total neutron yield (labeled “Yn”); line-integrated density is measured along individual HeNe 633 nm interferometry chords at various locations throughout the device (labeled “HeNe IF”); a Thomson scattering (labeled “TS”) system measures electron temperature and density at 17 locations across the device at a fixed axial location [1]; ion temperature, density and velocity is measured from Doppler broadening of impurity emission lines (labeled “IDS”); two dimensional density imaging is enabled via digital holographic interferometry (labeled “DHI”); an extreme ultraviolet spectrometer measures emission spectra in the 5–40 nm wavelength range for impurity identification, radiative power studies as well as plasma temperature and density measurements (labeled “EUV”); V-UV fast camera imaging is available at various view-ports along the device (labeled “Fast cam”) as well as a high frame-rate X-ray imaging detector (labeled “X-ray cam”). Finally, circuit diagnostics consist of the voltage measured across the electrodes (labeled “Vgap”) as well as the total plasma current across the electrodes as measured by a Rogowski coil, (labeled “Ip”). Various other diagnostic systems are under development, including a polarimeter for measuring the Faraday rotation of internal magnetic fields; a Zeeman spectroscopy system, also for internal field detection; and an x-ray crystal spectrometer for measuring properties of higher energy impurity lines.

2.2. Recent Experimental Results As Zap has grown into a larger company, we are now able to field two fusion platforms, each producing significant science output from their own suite of measurements. At an earlier phase in the company’s development, external collaborations funded by ARPA-E with national laboratory teams significantly accelerated our diagnostic capabilities. Fruitful examples of these interactions were a collaboration with Lawrence Livermore National Laboratory (LLNL) to field the SPMT detectors discussed above; a collaboration with Los Alamos National Laboratory (LANL) to field soft x-ray diagnostics as well as plasma fast imaging capabilities; an ongoing collaboration with University of Nevada Reno (UNR) to develop the EUV diagnostic discussed above; and finally a collaboration with Lawrence Livermore National Laboratory (LLNL) and UC San Diego to field a Thomson scattering diagnostic for measurements of Te and ne.

Recent campaigns focused on performing multi-point, time resolved Thomson scattering measurements [1] on the FuZE device. Electron temperatures in excess of 2 keV [2] were achieved simultaneous with neutron production and peak current, as shown in Fig. 3. This figure presents a slightly lower temperature shot with a ≈ 6 mm radial profile peaked at ≈ 1.4 keV. These results confirm earlier inferred Te measurements from soft x-ray measurements undertaken with LANL collaborators, Fig. 4. The inferred Te plotted in red results from taking the ratios of the transmission through two different filter materials and applying an assumption of a Maxwellian temperature distribution. This time resolved result provides a useful comparison to the single-time TS measurements, though the interpretation of the inferred Te from the soft x-ray diagnostic can be challenging due to contaminating x-rays generated from plasma wall interactions.

Another Zap Energy collaboration with LLNL deployed an array of neutron scintillators (top right panel of Fig. 5) used to measure the spatial and temporal details of the fusion production, calibrated neutron yields, and neutron energy spectroscopy, which can differentiate thermonuclear versus beam target contributions to the fusion yield. The right bottom panel of Fig. 5 shows that an extended source of ≈ 30 cm provides the best fit to the neutron measurements[3]. The left panel of the figure also shows a visible light image of the plasma consistent with this axial extent, taken by an optical fast framing camera provided by our LANL collaborators. (This frame is taken at an earlier time in the discharge than when neutron emission is peaked, when we typically observe maximum light emission in the V-UV range.) A further significant result from the SPMT detectors is discussed in Section 3, which addresses the observed and expected scaling of neutron yield as a function of the SFS Z pinch current.

3. SCALING VIA ADIABATIC COMPRESSION

A method of assessing the fusion performance of the experimental SFS Z-pinch platforms is against the projected scaling as pinch current is increased[13]. The Bennett relation[14], applicable to any Z pinch with radial force balance between magnetic (j × B) and thermal (∇p) forces, gives the temperature scaling, T ∝ I^2, where I refers to the current in the pinch, as distinct from Ip, which we designate as total plasma current in the device. Assuming adiabaticity (p ∝ n^γ) and taking γ = 5/3 leads to n ∝ I^3 and a ∝ I^(-3/2).[13, 11, 7] A “sharp pinch” model[15] is typically assumed in which the plasma has radially uniform density and temperature contained within radius a, where the confining current exists in an infinitesimally thin layer. Then, the D-D fusion rate in the sharp pinch with deuterium density nD = n is

\dot\{Y\}\{DD\} = \frac\{1\}\{2\} n^2 \langle \sigma v \rangle\{DD\} \pi a^2 L, (1)

where L is the plasma axial extent and ⟨σv⟩DD is the Maxwellian-averaged D-D fusion reactivity, which scales approximately as ⟨σv⟩DD ∝ T^4 from 1 to 10 keV.[16] (Notably, D-T reactivity also scales as ∝ T^4 in the 1 to 10 keV temperature range.) The overall adiabatic scaling of D-D fusion yield rate is then \dot\{Y\}_\{DD\} ∝ I^11 when assuming a constant linear density between equilibrium states.

Increasing the pinch current experimentally has demonstrated the corresponding increase in neutron yield, with DD yields Yn > 10^9 neutrons per pulse in the FuZE-Q device, which was recently commissioned. The neutron yields of both the FuZE and FuZE-Q devices are shown in Fig. 6(a) versus plasma current. (In general, the expected scaling relationship exists versus the pinch current itself, not the total plasma current. However, the total plasma current offers a more reliable measurement from a Rogowski coil compared to the more complex method for deriving the pinch current from the surface magnetic field probe array in the assembly region. Heuristically, we have found that the total pinch current measured at the peak neutron emission time, Ip(trad), is a conservative proxy for the pinch current. This is the measurement that is used in these plots.)

Neutron yield scales strongly with plasma current on both devices, though the larger available stored energy on the FuZE-Q cap bank is able to generate pinches with significantly higher pinch currents. Figure 6(a) consists of all pulses taken on both devices, without filtering for comparable pulse parameters. Figure 6(b) displays a subset of pulse for FuZE-Q taken with controlled parameter scan to study yield scaling versus current. The regression to this data set is consistent with Yn ∝ I^11 with an R^2 = 0.74, matching the expected I^11 adiabatic scaling (see Ref. [6] for details). These new results show that when mass inventory and gas injection characteristics are properly coupled to the current waveform, the expected neutron scaling with plasma current is observed.

4. EFFECT OF IMPURITY CONTENT ON PERFORMANCE SCALING

4.1. Scientific Gain Qsci with SFS Requirements The scientific gain Qsci of a SFS Z-pinch [17], is given by Eq. 2, where Pfusion is the DT thermonuclear fusion power, Pth is the thermal energy loss, Pflow is the flow power, Prad is the radiative power loss, and Pα is the redeposited alpha power.

Q_\{sci\} = \frac\{P_\{fusion\}\}\{P_\{IN\}\} = \frac\{P_\{fusion\}\}\{P_\{th\} + P_\{flow\} + P_\{rad\} - P_\{\alpha\}\} (2)

An equal population of deuterium and tritium is assumed, nD = nT = n/2 and that ion and electron temperatures are equilibrated, Te = Ti = T.

P_\{fusion\} = \frac\{n^2\}\{4\} \langle \sigma v \rangle_\{DT\} E_\{DT\} V_p (3) P_\{th\} = \frac\{3\}\{2\} (1 + \bar\{Z\}) \frac\{nT\}\{\tau_E\} V_p (4) P_\{flow\} = \frac\{1\}\{4\} (m_D + m_T) \frac\{n v_z^2\}\{\tau_\{flow\}\} V_p (5) P_\{rad\} = C_B Z_\{eff\} \bar\{Z\}^2 n^2 T^\{1/2\} V_p (6) P_\{\alpha\} = f_c P_\{fusion\} (7)

Note EDT ≈ 17.6 MeV is the energy yield per fusion event and the fusing plasma volume Vp = πa^2 Lp where a is the pinch radius and Lp is the pinch length. The form of the radiative power loss Prad assumes that Bremsstrahlung is the dominate loss mechanism, which is expected at the desired high gain operating points. Next, the Alfvén speed at r = a^+ is given by Eq. 8 in the “sharp-pinch” limit, immediately outside of the surface current at r = a in this model: v_A(a) = \frac\{B_\theta(a)\}\{\sqrt\{\mu_0 \rho\}\} \approx \frac\{B_\theta(a)\}\{\sqrt\{\mu_0 n m_i\}\} (8)

Using the Bennett relation given by Eq. 9 it is clear the Alfvén speed scales with the sound speed, given by Eq. 10: \beta = \frac\{2\mu_0 \langle p \rangle\}\{B_\theta^2(a)\} = \frac\{2\mu_0 (1 + \bar\{Z\}) n T\}\{B_\theta^2(a)\} = 1 (9) c_s = \sqrt\{\frac\{2T\}\{m_i\}\} = \frac\{v_A(a)\}\{\sqrt\{1 + \bar\{Z\}\}\} (10)

The importance of this relationship is accentuated within the context of SFS, which requires a sufficiently large radially sheared axial flow to mitigate the growth of virulent plasma instabilities [7, 11, 13]. The required flow speed for stabilization can be expressed as Eq. 11, assuming a linearly varying flow within r ∈ (0, a) and a coefficient Cm ∈ (0.1, 0.5) from both linear and nonlinear stability theory [12]. v_z(a) \ge C_m k a v_A(a) = C_m k a c_s \sqrt\{1 + \bar\{Z\}\} (11)

Saturating the inequality in Eq. 11 and substituting into the subcomponents of Qsci as applicable, the scientific gain Qsci is given by Eq. 12. Note that though fusing plasma volume Vp = πa^2 Lp is common to all terms, there is an explicit dependence on the pinch length Lp used to define the flow through time τflow = Lp / vz and correspondingly the energy confinement time τE ≈ τflow as done previously [17].

Q_\{sci\} = \frac\{\langle \sigma v \rangle_\{DT\} E_\{DT\}\}\{6(1 + \bar\{Z\})^\{3/2\} \frac\{T\}\{n L_p\} C_m c_s + (m_D + m_T) \frac\{(C_m c_s \sqrt\{1 + \bar\{Z\}\})^3\}\{n L_p\} + 4 C_B Z_\{eff\} \bar\{Z\}^2 T^\{1/2\} - f_c \langle \sigma v \rangle_\{DT\} E_\{DT\}\} (12)

4.2. Scaling to fusion conditions with impurities A pinch length of Lp = 0.5 m is used in this analysis, motivated by the length of the compression region on the FuZE and FuZE-Q devices. Plasma operating contours (POPCon) are provided in Fig. 7 for various cases of Zeff and fc. The canonical case of vz = 0.1vA and Z̄ = Zeff = 1 with a chosen adiabatic trajectory are plotted in Fig. 7(a) and (b), indicating scientific breakeven Qsci = 1 with a pinch current of approximately 650 kA. Higher flow speed requirements, such as a limiting vz = 0.5vA, would lead to larger required plasma pressures to reach a desired triple product pτE because of shorter flow through times τflow ≈ τE.

To compare to this pure hydrogenic case, an extreme case with impurities that limits the accessible Qsci ≈ 10 at a maximum pinch current Ipinch = 2 MA is given in Fig. 7(c) and (d), with Zeff = 4 and Z̄ = 2. This limiting example is an extreme case, and would constitute a 20% fully ionized carbon impurity in the otherwise deuterium. Even so, this scaling is given to demonstrate that a reactor relevant design point with Qsci is still possible even with significant impurity populations, but demanding higher density, temperature, and pinch current.

Additionally, redeposited alpha power can provide significant assistance in attaining high gains once entering the burning plasma regime Qsci ≈ 5 by reducing the required input power to balance both thermal and radiative losses. The same limiting case with Zeff = 4 is considered but with half of the generated alpha power being deposited into the plasma (i.e., fc = 0.1 in Eq. 12), as shown in Fig. 7(e) and (f). As expected, the scaling of the scientific gain is largely unchanged through breakeven, but then begins to diverge once alpha heating becomes a more dominate term in power balance. This assumed redeposition provides access to high gains Qsci > 10 with pinch currents below 1.5 MA and temperatures below 20 keV. Thus, redeposited alpha power tends to improve the tolerance of this concept to high impurity content by reducing the required input power to compensate for the increased radiative and thermal losses when compared to the canonical hydrogenic case given in Fig. 7(a) and (b).

5. CONCLUSION AND ACKNOWLEDGEMENTS

5. CONCLUSION The FuZE-Q device, along with its newly commissioned 1 MJ class current driver, is predicted to be able to generate Z-pinch discharges characterized by triple products meeting Lawson criterion. Assuming continued performance scaling as shown here, the SFS Z pinch would make a compact fusion power plant. The simplicity of the device, enabled by its lack of need for external magnetic confinement, allows for a robust and economical plant design. A fusion power plant based on the SFS Z pinch has strong advantages over other approaches in a variety of aspects including size, cost, simplicity, and safety.

Here we support these efforts with updates from the FuZE and FuZE-Q machines. Elevated electron temperature, neutron yields consistent with adiabatic scaling and an extended axial pinch volume, as well as a performance robustness to Zeff are steps to achieving the larger goal. As next efforts come online, including further advancements on our current drivers and upgrades to both FuZE and FuZE-Q, continued progress is anticipated.

ACKNOWLEDGEMENTS The information, data, or work presented herein was funded in part by the Advanced Research Projects Agency – Energy (ARPA-E), U.S. Department of Energy, under Award Nos. DE-AR-0000571, DE-AR-0001010, DE-AR-0001260 and by the Air Force Office of Scientific Research under Grant No. FA9550-15-1-0271. This research used resources of the National Energy Research Scientific Computing Center (NERSC), a U.S. Department of Energy Office of Science User Facility located at Lawrence Berkeley National Laboratory, operated under Contract No. DE-AC02-05CH11231. Prepared by LLNL under Contract DE-AC52-07NA27344, LLNL-PROC-854534.

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