Physical and technical basis of Materials Plasma Exposure eXperiment from modeling and Proto-MPEX results

The Materials Plasma Exposure eXperiment (MPEX) is a steady-state linear plasma device that will address plasma-material interaction (PMI) science and enable testing of fusion reactor-relevant divertor plasma-facing materials. The MPEX source concept consists of a helicon plasma source to generate the plasma, electron cyclotron heating (ECH) for electron heating, and ion cyclotron heating (ICH) for ion heating. The MPEX source plasma is then transported axially to the PMI material target region to test material samples in fusion reactor-relevant divertor conditions. This paper will summarize the physical and technical basis of MPEX. The paper will first define the MPEX parameters and scenarios at the target relevant to PMI science for various fusion reactor-relevant divertor conditions and show plasma transport modeling results to set the MPEX source parameters. Recent experimental and modeling results from Proto-MPEX, a short-pulse experiment to develop the plasma production, heating, and transport physics for MPEX, will be shown. From these results, it will be shown that MPEX can reach its desired scenarios. The MPEX physical and technical basis will also determine important functional requirements for magnetic field, radiofrequency (RF) power, RF frequency, and neutral pressure in the helicon, ECH, ICH, and PMI regions that are required to achieve the desired MPEX scenarios. The necessity for key in-vessel components such as skimmers, limiters, and microwave absorbers will also be highlighted.


Introduction
Plasma-material interactions (PMI) have been identified as an important issue for obtaining a high performance, high dutycycle and safe operating fusion reactor in published papers [1][2][3], reactor design studies [4][5][6] and community reports [7][8][9]. Some of the scientific challenges include power handling capability of plasma facing components, erosion and redeposition, tritium retention, neutron activation, and power extraction. One of the major technical challenges of PMI is that no existing facility can reproduce expected fusion-reactor relevant divertor conditions to study the relevant PMI science, particularly those at high ion fluences with neutron activated materials. Existing tokamaks and toroidal confinement devices are limited in their pulse lengths and ion fluences, and existing linear devices are limited either in their ion flux, ion fluence, plasma transport regime in front of the material sample, and/or the ability to test neutron activated material samples. The goal of the Materials Plasma Exposure eXperiment (MPEX) [10][11][12] is to enable steady-state testing of plasma facing materials for fusion reactor-relevant divertor conditions such as ion fluxes >10 24 m −2 s −1 , parallel heat fluxes up to ∼40 MW m −2 , and ion fluence up to 10 31 m −2 . MPEX is a steady-state linear plasma device that will have the capability to investigate solid plasma facing materials, liquid metals, and neutron activated materials from the High Flux Isotope Reactor [13] or a fusion prototypic neutron source. MPEX will use a novel radiofrequency (RF) source concept with helicon plasma source to produce the plasma density, electron cyclotron heating (ECH) for heating electrons, and ion cyclotron heating (ICH) for heating ions. Because of this RF source concept, MPEX will have independent control of the plasma electron and ion temperature and also have the capability to mimic a realistic Chodura sheath for magnetic field incident angles of a few degrees to the material sample. MPEX will also have the capability to access a range of expected fusion reactor-relevant divertor conditions from fully detached to partially detached to conduction limited to sheath limited divertor regimes.
The goal of this paper is to summarize the MPEX physical and technical basis to demonstrate that MPEX can achieve its scenarios and to determine functional requirements for the magnetic field, neutral pressure, RF power, RF frequency, and needed in-vessel components on MPEX. This paper largely details recent, new Proto-MPEX experimental and modeling results. Some older experimental and modeling results have been re-analyzed and updated. The MPEX physical and technical basis strategies largely focus on the Proto-MPEX experiment in comparison to MPEX source parameters. The most desirable strategy is to use Proto-MPEX data that corresponds one to one with expected MPEX source parameters. This has been mostly achieved for the helicon plasma source. When this is not possible such as with electron and ion heating, the MPEX physical and technical basis strategy is to validate physics-based models on Proto-MPEX and then use it to predict functional requirements on MPEX. If this strategy is not possible, which can occur if there is not a reliable physicsbased model, a linear extrapolation is done to scale from Proto-MPEX to MPEX parameters.
An outline of the paper is as follows. Section 2 focuses on the required MPEX parameters at the source and target. Section 2.1 outlines the target parameters that are set by MPEX science goals. Section 2.2 shows the plasma transport modeling from the source to the MPEX target that sets the MPEX source parameters. Section 3 discusses Proto-MPEX experimental results with a major focus on the helicon plasma source, helicon + ECH operation, helicon + ICH operation, and combined helicon + ECH + ICH operation. Section 3.1 briefly describes the Proto-MPEX experiment. Section 3.2 shows Proto-MPEX results for the helicon antenna, section 3.3 shows Proto-MPEX results for ECHand section 3.4 shows Proto-MPEX results for ICH. Section 3.5 shows results for combined helicon + ECH + ICH operation to demonstrate that the heat flux for simultaneous operation of plasma production and heating schemes is equal to the total heat fluxes for individual plasma production and heating schemes. Sections 4. 1-4.4 show that the Proto-MPEX results can extrapolate to the desired MPEX target plasma density, electron temperatures, ion temperatures and heat fluxes, respectively, and achieve its scenarios. Section 4 also show how plasma production, heating, and transport physics learnt from Proto-MPEX specifies functional requirements for the magnetic field, neutral pressure, RF power, RF frequency, and needed in-vessel components in the helicon, ECH, ICH, and PMI regions of MPEX. Section 5 summarizes the results and concludes the paper.

MPEX parameters at target
To access fusion reactor-relevant divertor conditions on MPEX, four goal scenarios (High n e , High p e , High T e , and Low n e ) have been developed and are shown in table 1 at the material sample target location. By using a B2.5-EIRENE database of different ITER scenarios and divertor regimes [14], these MPEX goal scenarios were chosen to mimic expected ITER divertor density and temperature conditions form sheath limited to conduction limited to partially detached to fully detached divertors. The requirements for the plasma diameter are chosen due to PMI science considerations to be larger than characteristic length scales such as ionization mean-free-paths perpendicular to the magnetic field, ion gyroradius, and confinement length scales [10]. This is so that non-dimensional PMI science length scales relative to the plasma size is similar on MPEX and ITER even for different magnetic field magnitudes [15]. MPEX is also designed to run up to 10 6 s (∼10 d) to enable testing material samples for ion fluences up to approximately 10 31 m −2 that is 1000 times longer than the expected 1000 s pulse duration of an ITER discharge and significantly moves towards ion fluences in a future fusion reactor divertor. Table 1 shows the required MPEX scenarios at the material target. The plasma production and heating antennas are however not located at the target, so the plasma needs to be transported axially from the plasma production and heating regions to the target and PMI region to achieve the target MPEX scenarios. Therefore, the MPEX source n e , T e , and T i are required to determine functional requirements at the helicon, ECH, and ICH regions. Multiple plasma transport models were used to predict the source plasma conditions for the desired target MPEX scenario parameters. These models range in physics fidelity and computational complexity. These include analytical two-point models [16], 2D plasma transport models (B2.5-EIRENE [17]) for targets normal (90 • ) to the magnetic field, and 3D plasma transport models (EMC3-EIRENE [18]) for tilted targets inclined near parallel (5 • ) to the magnetic field. Tilted targets are of interest to fusion reactor-relevant divertor scenarios since magnetic fields lines in a reactor divertor will be inclined nearly parallel to the target:

MPEX parameters at source
For conduction-limited regimes, the two-point model [16] predicts that the density at the target, n t , depends on the density at the source, n s , parallel heat flux, q || , length between the source and target, L, power loss factor, f -power and a momentum conservation factor f -mom. This is shown in equation (1). If the power loss factor is ignored and the momentum conservation factor is equal to 1, this constitutes a simple two-point model that assumes constant pressure along field lines. In the High n e MPEX scenario, however, where the target electron temperature will be less than 3 eV, momentum loss will take place due to charge exchange and possibly even three-body recombination. This effect can be taken into account in the two-point model by introducing a power loss factor and momentum conservation factor. Both factors depend strongly on atomic physics and are strong functions of the electron temperature as well as the neutral density and impurity density.
To calibrate the power loss and momentum conservation factors and investigate how the target parameters depend on source parameters for MPEX, a B2.5-EIRENE cylindrical model of length L with constant magnetic field and an input plasma ion flux was used. For the parameter scans, the source ion flux was varied between 2 × 10 20 -2 × 10 21 s −1 . The source power flux was varied between 100 and 500 kW. The heating was assumed to be 90% into electrons and 10% into ions. The source profiles are assumed to be Gaussian. Pumping was imposed on an annulus at either the source end or the target end or along the side of the vacuum wall. The pumping locations were varied as well as the reflection coefficient of the particles. The radial transport is assumed to be diffusive, and described by typical anomalous particle and heat diffusivities, D, χ = 0.75 and 1.5, m 2 s −1 , respectively. No plasma impurities are assumed.
Results are shown in figure 1. Using this cylindrical model, power loss and momentum conservation factors are fit as a function of the source density and flux. The momentum conservation factor depends only weakly on the upstream heat flux and device length. The momentum conservation factor mainly depends on the upstream particle flux and therefore mainly on the upstream density. The power loss factor also depends only weakly on the device length and the upstream power density. Like the momentum conservation factor, the power loss also depends mainly on the upstream particle flux and the upstream density.
These fits of the power loss and momentum conservation factors are then used to calculate how the target parameters depend on the source parameters. This was done using a B2.5-EIRENE model with an example MPEX magnetic and vacuum geometry. It is assumed that there are 200 kW helicon antenna, 100 kW ECH, and 200 kW ICH power absorbed in this model. The helicon, ECH, and ICH locations are approximately located at 1.2, 2.2, and 3.5 m, respectively. Pumps are located at the helicon, ECH, and target regions. Gas puffing can be  B2.5-EIRENE density and temperature for gas puffing at the helicon region for high Te scenario. MPEX dump plate is at z = 0 m and target is located at z ∼ 8 m. The helicon, ECH, and ICH locations are approximately located at 1.2, 2.2, and 3.5 m, respectively. applied at the helicon or target locations. The dump plate is located at 0 m and the target at approximately 8 m. Figure 2 shows the result for the density and electron temperature onaxis for gas puffing at the helicon region. For puffing at the helicon antenna location, the electron density is relatively symmetric. The peak density is about 25% higher in front of the target compared to just in front of the dump plate. The target density is about a factor of 1.5 higher than the dump plate density. The pressure increases from the helicon location at Z = 1 m along the other heating location and remains relatively constant along the axis towards the target at Z = 8 m. The pressure at the dump at Z = 0 m drops strongly mainly due to the magnetic flux expansion in front of the dump plate. In front of the target, n e ∼ 2 × 10 20 m −3 and T e ∼ 10 eV. These are exactly the required parameters for the MPEX High T e goal scenario in table 1. It should be noted that these results were similar to simpler estimates from two-point model and the cylindrical B2.5-EIRENE model so the plasma transport physics here is reasonably well understood from the twopoint model. The results are achieved with a distance between the source and target of approximately 5 m. Figure 3 shows the axial electron density for gas fueling at the target. The peak electron density in front of the target is close to 2 × 10 21 m −3 and the target electron temperature is close to 2 eV. This is close to the required parameters for the High n e goal scenario in table 1. The temperature profiles show a peak in the respective heating section and drop off to both sides at the target and the dump plate. The electron temperatures are reduced to 1-2 eV at the target, as expected for such a high density. In this case, the pressure along the axis increases by a factor of 3 near the target at z ∼ 8 m, which makes thing difficult to interpret and understand based on simple analytical models [16]. It is hypothesized here that the cause of the pressure increase is related to the parallel viscosity term in the  Braginskii momentum balance equation. The magnetic ripple due to the magnetic mirrors in the heating sections and the plasma parallel flow from the target to the dump may also be partly responsible for the strong increase of the pressure and density at the target. It is further hypothesized that additional plasma production and heating power from helicon, ECH, and ICH may allow for improvement of the parameters on this scenario.
B2.5-EIRENE is a 2D model so it can only model axisymmetric systems and cannot capture the effects of a tilted target. EMC3-EIRENE simulations were adopted to allow for linear device modeling where 3D geometry is required [19]. Simulations were carried out for a linear geometry terminated at one end with a dump plate positioned normal to the magnetic field and a target on the other side where the angle to the magnetic field was varied. The radial transport is again assumed to be diffusive, and described by typical anomalous particle and heat diffusivities, D, χ = 0.75 and 1.5, m 2 s −1 , respectively. No plasma impurities are assumed. 300 kW of power is deposited at the axial center at Z = 0 m, divided equally between ions and electrons.
Two cases were investigated: normal incidence target (90 • ) and shallow angle of incidence (5 • ) for the high T e goal scenario. Results are shown in figure 4 where the axial dependence of T e and n e is shown. The dump plate is positioned at axial position 0 and the target at axial position 4.2 m. Again, the  15 20 profiles are symmetric when the target is positioned at 90 • . The EMC3-EIRENE results for this 90 • case have reasonably similar density and temperature profile magnitude and shape to the B2.5-EIRENE results. When the target is tilted to 5 • , the density in front of the target on axis is reduced by about 30% compared to the 90 • case. In contrast, the temperature is increased on axis for the 5 • case relative to the 90 • case. These results may be because that with a tilted target, the reionization of the plasma results in a plume that is tilted off-axis from the plasma. In a normal target, this reionization is centered onaxis of the plasma. The on-axis density may therefore be less for a tilted target than a normal target. For a high density, low temperature plasma scenario, the ionization mean free path is much smaller, and this effect might be more pronounced for high-density, low-electron-temperature plasmas.
Beside these plasma transport model predictions for MPEX, B2.5-EIRENE model has also been extensively used to study Proto-MPEX high density helicon plasmas [20]. This modeling demonstrated reasonable agreement with experimental measurements of plasma density, temperature, D α emission, flows [21], and parallel particle and power fluxes [22] at various axial locations [23]. This provides an important constraint on the perpendicular transport that is a key assumption of the B2.5-EIRENE model and therefore affects model prediction results.
A summary of these analytical two-point model, B2.5-EIRENE, and EMC3-EIRENE results is shown in table 2 to calculate the required source parameters for the high p e , high T e , high n e scenarios, and low n e MPEX 5 • and 90 • target scenarios. There are caveats to the calculation in table 2. Due to numerical reasons, B2.5-EIRENE calculations were done only for high T e and high n e scenarios with the target at 90 • and EMC3-EIRENE calculations were achieved only for high T e case with the target at 5 degrees. Simpler models such as the two-point model were used for the other cases assuming sheath limited and conduction limited regimes. Given the difference between untilted and tilted targets, a conservative factor of approximately 1.5 times the untilted case was assumed in the density for all the other tilted cases for high p e , high T e and high n e target cases based on the EMC3-EIRENE calculation. The B-2.5 EIRENE and EMC3-EIRENE calculations assume between 4-5 m between the source and target. A distance of 5 m is therefore chosen between the source and target for MPEX. Both models also have a conservative assumption on the total power and assume less power than the total available power on MPEX that will be further discussed later in this paper. These plasma source requirements set requirements for n e , T e , and T i at the helicon plasma source, ECH electron heating, and ICH ion heating regions. To be conservative and satisfy the requirements for all the scenarios, a minimum n e = 1 × 10 20 m −3 , T e = 30 eV, and T i = 30 eV is required at the MPEX source.

Introduction to proto-MPEX
To demonstrate that MPEX can achieve the desired target densities, electron temperature and ion temperature and to develop the plasma source concept, a proof of principle experiment called Proto-MPEX [24,25] was operated between 2014 and 2021. Proto-MPEX has relatively short pulses (<2 s) so it is not relevant to many fusion reactor-relevant PMI timescales of interest. Proto-MPEX also has relatively low available RF + ECH power (<330 kW) and relatively short distance (∼1 m) between the source and the target so that Proto-MPEX has not been able to access detachment regimes in deuterium plasmas at the target [26]. Therefore, studies on Proto-MPEX are not representative of MPEX target parameters. Studies on Proto-MPEX are relevant to the MPEX source and are therefore intended to understand the MPEX plasma production, heating, and transport physics and better develop the MPEX source concept.
A schematic of Proto-MPEX is shown in figure 5 including the Last Uninterrupted Flux Surface (LUFS) for an example plasma discharge. Various components such as the dump plate, gas puffing actuators, magnetic field coils, plasma production and heating antennas, skimmers, and the target are shown here. For a few experiments, a helicon limiter, which is not shown in figure 5, was also used. Proto-MPEX also has various diagnostics [24] such as baratrons to measure the neutral pressure at various axial locations, Langmuir probes [27] and Thomson scattering [28] to measure density and electron temperature at various axial and radial locations, Mach probes [29] to measure plasma flows at various axial and radial locations, filterscopes, cameras and spectrometers [30] to measure D α emission and other impurity lines at various axial locations, argon spectroscopy [31] to measure the ion temperature at various axial locations and an IR camera [32] to measure the 2D surface heat flux profile at the helicon window and target. These axial locations include measurements adjacent to the Proto-MPEX helicon antenna, ECH launcher, ICH antenna, and PMI target region.

Helicon plasma source
Helicon sources have been widely used to produce plasmas in linear plasma devices [33]. Proto-MPEX uses up to 200 kW, 13.56 MHz transmitter [34,35] transmitted into a Nagoya type III antenna to generate plasma densities in the helicon region. Helicon waves are fast waves with frequencies much larger than the ion cyclotron resonance frequencies. They can be absorbed by collisions and other processes and can efficiently produce plasmas in linear plasma devices. Previous experiments [34,35] on Proto-MPEX have used up to 100 kW of helicon power. This paper details recent experiments where up to 200 kW of helicon power has been achieved. Because of the higher helicon power, higher densities are created. This is shown in figure 6 where stable, high-density plasmas can be created with approximately 125 kW of net helicon power. Plasma densities of approximately 1.5 × 10 20 m −3 have been observed on the Proto-MPEX target.
One of the advantages of higher helicon powers is that it allows helicon antennas to excite helicon modes at higher magnetic fields. Helicon modes require transitions from inductively coupled or capacitively coupled modes and are often experimentally confirmed when the plasma density is proportional to magnetic field [36]. Previous experimental [34] and modeling [37] results on Proto-MPEX have shown that the core target density actually decreases with increasing helicon magnetic field >.08 T. This decrease in core target density is correlated with significant edge heating [38], likely because the Trivelpiece-Gould mode is excited. At that time, it was suggested that higher helicon powers >100 kW are necessary. Recent experimental results shown in figure 7 confirm that helicon modes can be established for helicon magnetic fields <0.2 T. This is done by varying the magnetic field everywhere using a fixed 125 kW of net helicon power. By varying the magnetic field everywhere, the plasma diameter and LUFS is fixed, which allows for unambiguous analysis related to magnetic flux expansion. As the magnetic field increases, the density measured at the target increases, as expected in a helicon mode. The highest densities are measured for the highest helicon magnetic fields. Densities up to approximately 1.5 × 10 20 m −3 are observed. Higher helicon magnetic fields also have other benefits. A higher helicon magnetic field leads to a larger target plasma diameter since the LUFS strikes the vacuum vessel in the helicon region. Larger diameters are desired for PMI science as the plasma diameter should be larger than characteristic PMI scale lengths of interest. A larger magnetic field will also reduce the helicon ionization cost and improve the ionization efficiency [39].
One of the challenges of producing high density deuterium plasmas with helicon sources in many linear plasma devices is that a non-uniform magnetic field profile is often required [40,41]. Figure 8 shows recent experiments on Proto-MPEX that illustrate the requirement for magnetic mirror fields similar to previous experiments in other linear plasma devices. By varying the helicon mirror magnetic field approximately 30%-40%, the density measured at the target by more than a factor of 2-2.5. While not shown, if the helicon mirror magnetic field is too small, no helicon high-density plasma is generated. Increasing helicon mirror fields also reduces the neutral pressure at the ECH launcher location and provide differential pumping between the helicon section and heating sections. This is because more efficient helicon plasma production improves the ionization efficiency and decreases the neutral density. This leads to lower neutral pressures in the ECH region [35]. This is important as the neutral pressure in the ECH and ICH regions have to be small to enable ECH and ICH heating. Besides the helicon mirror magnetic field, magnetic shaping fields are desirable. Figure 9 shows the results for a magnetic shaping scan upstream of the helicon antenna. By increasing this helicon shaping magnetic field at approximately z = 1.5 m, the plasma density measured at the Proto-MPEX target increases by a factor of 2. This shows that asymmetric magnetic fields around the helicon region benefit helicon plasma production.

ECH
Proto-MPEX uses up to a 200 kW, 28 GHz gyrotron transmitted into a corrugated waveguide launcher to heat electrons [42]. The baseline electron heating scheme is O-X-B Electron Bernstein Wave (EBW) heating that has previously been demonstrated in many plasma physics and fusion experiments [43]. This scheme launches the microwaves in the O-mode on the low magnetic field side, reflects off the O-cutoff and mode converts to the X-mode, reflects at the Upper Hybrid (UH) resonance layer and mode converts to a Bernstein wave before being absorbed by Doppler-shifted electron cyclotron resonance [44] at an appropriate cyclotron resonance layer. O-X-B EBW heating is useful at high densities where overdense heating with densities greater than the O-mode cutoff density is required. For relatively low temperature plasmas, O-X-B heating also has the advantage of high single pass absorption at the fundamental electron cyclotron resonances or higher harmonics of the electron cyclotron resonance. For MPEX, as discussed later in this paper, 2nd harmonic O-X-B EBW heating is chosen as the baseline heating scheme for the High n e , High p e , and High T e scenarios. These scenarios require the highest source densities and temperatures and are representative of conduction limited, partially detached and fully detached divertor scenarios that are expected in many future fusion reactor studies. Therefore, O-X-B EBW heating is the major focus of this paper. The low n e MPEX scenario requires under-dense electron heating schemes and multiple alternative schemes will be briefly discussed in the next section.
The first consideration for O-X-B EBW heating on Proto-MPEX and MPEX is the neutral pressure at the ECH location. Figure 10 shows the electron temperature measured at the ECH location as a function of neutral pressure on Proto-MPEX. If the neutral pressure is too high, there is little to no electron heating. If the neural pressure is low, electron heating is observed. Based on GENRAY-C ray tracing modeling results, this electron heating dependence on neutral pressure is expected to be due to collisional absorption of the Bernstein wave near the UH resonance layer [45]. Figure 11 shows recent experimental results for EBW heating for a 28 GHz ECH power scan applied using the upgraded helicon power up to 200 kW. Using 80 or 120 kW helicon power on Proto-MPEX, density, temperature and pressure was measured at the target. For increasing power, the density, temperature and pressure increases accordingly.   and electron plasma production using the 28 GHz gyrotron. It is speculated that if neutral pressure is even lower in the ECH region, there will be more electron heating and less plasma production due to fewer electron-neutral collisions and ionization events.
All these experiments with O-X-B EBW heating have been most successful in 'downhill' magnetic field configuration rather than 'overhill' magnetic field configuration. Larger electron heating is observed at the Proto-MPEX target for 'downhill' configurations. These magnetic fields are shown in figure 12 in the red line. Figure 12 also shows recent modeling using a Monte Carlo code [46] for non-thermal electrons, as evidence by significant perpendicular and parallel velocities compared to Maxwellian distribution at different axial locations on MPEX. These high perpendicular velocities are the result of electron cyclotron resonant heating that heats the electrons perpendicular to the magnetic field. Large parallel velocities can be the result of pitch angle scattering, thermalization, and slowing down by collisions as well as magnetic mirror trapping of particles. The mirror trapping is largely dominated at approximately z = 3.2 m where the electron cyclotron resonance occurs in both overhill and downhill configurations. This suggests non-thermal electrons are largely localized in the EBW heating location for both overhill and downhill configurations. For the downhill configuration, the non-thermal electron population is preferentially transported downstream to the PMI target region at z ∼ 4.15 m. For the overhill configuration, the non-thermal electron population is preferentially transported upstream to the helicon region. No non-thermal power is therefore transported to the target in the overhill case. For PMI science at the material target, this suggest that downhill magnetic field configuration is more favorable for O-X-B EBW heating and that that the magnetic field in the ECH, ICH, and PMI regions should have minimal magnetic field ripples with the magnetic field in ECH region > magnetic field in the ICH region > magnetic field in the PMI region to minimize magnetic trapping effects. These experiments for O-X-B EBW heating were also only successful near the 2nd electron cyclotron harmonic resonance. Figure 13 shows the result for a scan of ECH magnetic field with and without ECH power. Both core target heat flux and core electron heating are observed with ECH power for a ECH magnetic field near 0.5 T, which is the magnetic field at the 2nd harmonic cyclotron resonance for 28 GHz. No significant core electron heating or core heat flux was observed at the fundamental cyclotron harmonic when ECH power is turned on. GENRAY-C modeling suggested that for fundamental cyclotron resonances, the heating is largely in the edge plasma due to electron neutral collisions of the Bernstein wave near the UH resonance layer [45].

ICH
Proto-MPEX uses up to 30 kW, 6-9 MHz source transmitted into a modified Nagoya type III ICH antenna [47] to heat ions. In initial experiments, the intended ion heating scheme is a magnetic beach heating scheme where the slow wave is launched on the high magnetic field side before propagating and absorbing at the fundamental ICH resonance location [48]. The theoretical dispersion relation for the fast and slow wave is shown in equations (2) and (3) where R, L, P and S are the Stix plasma tensor using a warm plasma dispersion relation with a first order Larmor radius expansion [49], k || is the parallel wavenumber, and k ⊥ is the perpendicular wavenumber. .
(3) Figure 14 shows two example of this dispersion relation for realistic Proto-MPEX ICH parameters on Proto-MPEX: k || = 20 m −1 , antenna frequency = 6.5 MHz, and T i = T e = 10 eV deuterium plasmas for a range of relevant densities. In the top subfigure, the magnetic field is 1 T. In the bottom subfigure, the magnetic field is 1.4 T. For the magnetic field = 1 T case, this warm dispersion relation shows both the fast wave and slow wave branches. The fast wave has a cutoff where it only propagates above a certain cutoff density that is approximately 8-9 × 10 18 m −3 for this case. There is a confluence of the fast and slow wave for density at approximately 1.3 × 10 19 m −3 known as the Alfvén resonance. At the Alfvén resonance, mode conversion can also occur between the slow and fast wave. The low-density slow wave branch is commonly called the inertial Alfvén wave. The high-density slow wave branch is commonly called the kinetic Alfvén wave and only exists with the inclusion of finite electron temperature effects in the dispersion relation. When the magnetic field is increased to 1.4 T, the qualitative picture remains the same. However, the fast wave cutoff and Alfvén resonance are shifted to higher densities.
Because this dispersion relation includes a first order Larmor radius expansion of the hot plasma dielectric tensor, it includes electron Landau damping and fundamental ion cyclotron resonant damping effects. This warm dispersion relation is then used as the plasma dielectric tensor in a 2D COMSOL model [50] that captures realistic magnetic field geometry and vacuum vessel geometry. Figure 15 shows the results of this recent COMSOL modeling effort for two different Proto-MPEX magnetic field profiles with ICH antenna magnetic field = 1 and 1.4 T. Also, cases are shown assuming either a primarily slow wave launch (antenna current is assumed in the axial direction parallel to the applied magnetic field) or a primarily fast wave launch (antenna current is assumed in the azimuthal direction perpendicular to the applied magnetic field). For the simulation with primarily slow wave launch, the power absorbed is only in the edge and minimal heating is observed at the fundamental ICH resonance location. For the simulation with primarily fast wave launch at ICH antenna magnetic field = 1 T, some electron heating is still observed in the edge but strong heating is also observed in the core at the ICH resonance. Further analysis shows that the edge heating of the slow wave is due to electron Landau damping and the core heating is due to fundamental ICH from the slow wave. For pure deuterium plasmas, fast waves have the wrong polarization and cannot absorb at the fundamental ion cyclotron resonance layer. The slow wave, however, can damp with high single pass absorption at the fundamental ion cyclotron resonance. The modeling also shows that a launched fast wave is required for core ion heating. This suggests that the ion heating is due to a launched fast wave that is mode converted to a slow wave. For the simulation with primarily fast wave launch at ICH antenna magnetic field = 1.4 T, heating is still observed in the core at the fundamental ICH resonance, but it is significantly less than the case with magnetic field = 1 T. The analysis suggests these differences are largely due to the distance between the antenna and fast wave cutoff layer, which increases with magnetic field from the dispersion relation analysis. This leads to a decrease in antenna loading as the launched fast wave is evanescent and must tunnel a further distance before propagation [51]. This simulated core ion heating is consistent with trends from experimental measurements and further details are in [49]. Figure 16 shows experimental results for the measured core ion temperature near the ICH antenna as a function of ICH power. As ICH power is increased, the ion temperature increases linearly. Figure 16 also shows the core heat flux observed at the target. As the ICH power increases, the core heat flux increases. The increase with heat flux and ion temperature is approximately linear with respect to ICH power up to an ICH lower level of 25 kW, which supports a linear RF heating mechanisms such as that the abovementioned linear COMSOL model. Recent results also show good agreement between COMSOL modeling and ICH experiments on Proto-MPEX [49] for power absorption as a function of ICH magnetic fields. This provides further confidence that the above-mentioned ICH heating scheme and COMSOL model is valid on Proto-MPEX and can be used to model MPEX.

Combined helicon plasma source, electron heating, and ion heating
Proto-MPEX has recently conducted a few experiments with combined helicon + ECH + ICH operation. Target n e , T e , and T i was not directly measured for combined operations as a function of input power. However, the heat fluxes have been experimentally shown to be additive for helicon-only, helicon + ICH, helicon + ECH, and helicon + ECH + ICH operations on Proto-MPEX. This is shown in figure 17 with core heat flux measurements for 90 kW of helicon-only operation, 90 kW of helicon + 35 kW of ECH operation, 90 kW of helicon + 25 kW of ICH operation, and 90 kW of helicon + 25 kW of ICH + 35 kW of ECH operation. With simple arithmetic, the individual contributions of helicon-only, ICHonly, and ECH-only can be determined and can be calculated to be very close to the heat flux measured with combined operations.

MPEX source density
As shown in figure 7, the measured Proto-MPEX target densities are larger than the required MPEX source n e = 1 × 10 20 m −3 . Therefore, the requirements for the helicon region on MPEX are similar to those on Proto-MPEX. These densities were achieved for helicon magnetic fields less than 0.2 T at the helicon region on Proto-MPEX, which sets the helicon magnetic field requirement for MPEX. Each of the MPEX magnetic coils are individually powered so that non-uniform magnetic field profiles such as helicon magnetic mirrors and magnetic shaping fields can be achieved on MPEX. Proto-MPEX and MPEX has expected neutral pressures between 0.1 and 3 Pa in the helicon region [52] to satisfy the helicon region neutral pressure requirement. This is due to the large neutral pressures needed to ionize the neutral gas in this region to create plasma. Based on these existing results using less than 200 kW of helicon power on Proto-MPEX, 250 kW of helicon source power with the existing 13.56 MHz frequency is conservatively planned for MPEX to achieve the necessary plasma source n e . Because the two-point model in equation (1) has the target n e proportional to the cubic power of the source n e , there is considerable benefit to have a conservative estimate for higher helicon powers and a large source n e in increasing the target n e .
One concern on MPEX that was not a concern for Proto-MPEX is steady-state heat loads on the MPEX helicon window. In these experiments shown in figures 7-9, the LUFS intersects directly on the helicon window because of the relatively low magnetic field at the helicon location. The helicon antenna is located radially outside the helicon window, so the helicon window must be transparent to the helicon wave fields, maintain vacuum integrity, and withstand plasma heat fluxes. The dielectric material choice and helicon window design can be challenging [53] and it is desirable to have low plasma heat fluxes incident on the helicon window. For short pulse operation on Proto-MPEX, these are not significant constraints. For steady-state discharges on MPEX, however, these constraints are important and it is therefore required that the LUFS does not intersect directly on the MPEX window so that the incident plasma flux is reduced. A helicon limiter is therefore required on MPEX to allow the LUFS to be directly incident on the helicon limiter rather than the helicon window. Previous experiments on Proto-MPEX [54] have shown that the introduction of a helicon limiter adjacent to the helicon window, as shown in figure 18, can move the LUFS onto the limiter and reduce the heat flux incident on the helicon window while maintain high helicon plasma production. Some incident heat flux, however, is still observed on the helicon window with the addition of the helicon limiter. This is because photon flux, charge exchange neutral fluxes, and ion acceleration mechanisms such as RF sheaths [55] are partly responsible for the incident heat flux and are not modified with the addition of a helicon limiter. A conceptual design for the helicon limiter and skimmers is shown in [56].

MPEX electron temperature
As shown in figure 11, the maximum target electron temperature achieved on Proto-MPEX is approximately 10 eV and this is not sufficient for the required MPEX source T e = 30 eV so more ECH power is needed for MPEX. Using the results of figure 11, a linear extrapolation is therefore done using the plasma pressure. The pressure is chosen as the metric because ECH power modifies both density and temperature. The goal is to reach the source requirement in table 2 of n e = 1 × 10 20 m −3 and T e = 30 eV for all MPEX scenarios. This is equivalent to an electron pressure of 500 Pa for MPEX. Magnetic flux expansion needs to be considered to compare this Proto-MPEX discharge to MPEX. On MPEX, the magnetic field at the ECH region is 1.25 T. For this Proto-MPEX discharge, the magnetic field at the ECH region is 0.25 T. Therefore, the desired electron pressure at the Proto-MPEX target is 500 * √ 0.25/1.25 = 222 Pa. Based on linear extrapolation to T e = 30 eV for 120 kW helicon power case in figure 11, this is estimated to be 350 kW of EBW power. A conservative 400 kW of ECH source power is planned on MPEX to meet the MPEX source T e requirements.
The Proto-MPEX results in figure 10 also suggest that the neutral pressure in the ECH region on MPEX <0.01 Pa for electron cyclotron absorption of the Bernstein wave. This also suggests that it is important to have large helicon mirror magnetic field ratios such as those shown in figure 8 to reduce the neutral pressure in the ECH region. Because there is a large neutral pressure difference in requirements between the helicon and ECH regions, skimmers were used on Proto-MPEX and are required on MPEX to increase differential pumping between the helicon and ECH regions [57]. Because the neutral gas is largely ionized in the core plasma, the neutrals are predominantly located in the edge plasma of a linear device. Skimmers largely prevents axial transport of neutrals between the helicon and ECH by blocking the edge plasma. Skimmers have an opening in the main plasma, which allows plasma transport between the helicon and ECH regions. Because of the need 2nd harmonic heat, downhill" magnetic field configuration with magnetic field at ECH region > magnetic field at the target and the required 1 T magnetic field at the target for many MPEX scenarios, the magnetic field at the ECH region > 1 T. Based on the available frequencies for high-powered gyrotron, a dual-frequency gyrotron was chosen on MPEX at frequency = 70 and 105 GHz with a baseline ECH magnetic field of 1.25 T for 2nd harmonic O-X-B EBW heating. The magnetic field for 2nd harmonic electron cyclotron resonance for gyrotron frequency of 28 GHz and 53 GHz gyrotrons is less than 1 T at the ECH region and insufficient for MPEX requirements. This is shown in more detail in table 3.
The O-X-B EBW baseline electron heating scheme only works for over-dense densities above the O-mode cutoff density when the O-mode cutoff layer exists. At 70 GHz, the Omode cutoff density is 6 × 10 19 m −3 , so other electron heating schemes will be required for source n e below 6 × 10 19 such as the MPEX Low n e scenario. Three under-dense alternative heating schemes are envisioned on MPEX: UH heating at 70 or 105 GHz, 2nd harmonic X-mode electron cyclotron resonance heating at 105 GHz, and whistler wave heating at 70 GHz. The UH heating scheme uses collisional heating near the UH resonance layer, which depends on the magnetic field and density. By modifying the magnetic field, the heating can be adjusted for different densities in the under-dense heating range. This heating scheme has previously been demonstrated on Proto-MPEX [58]. Based on these previous experimental results, power extrapolation similar to what was done previously for O-X-B EBW heating suggests that approximately 300 kW ECH power is required for under-dense UH heating at these lower density MPEX scenarios. Based on the experimental data, upper hybrid heating appears approximately two times less efficient than O-X-B EBW heating. Luckily, this is sufficient for the Low n e and one of the high T e scenarios.
Second harmonic X-mode electron cyclotron resonance heating scheme is commonly used as an electron heating scheme for under-dense fusion plasmas at fusion-relevant temperatures ∼10 keV [59]. The single pass absorption and optical thickness for this heating scheme depends strongly on the magnetic field gradient, plasma density and plasma temperature [60]. An estimate is shown in figure 19 using theoretical calculations [60] and GENRAY-C modeling for MPEX and fusion reactor temperatures. As expected in a fusion reactor where electron temperatures on the order of 10 keV, the single pass absorption is very close to 1, For MPEX, where the temperatures are much lower than in a fusion reactor, the single pass absorption is much lower and is on the order of a few percent. This makes this 2nd harmonic X-mode ECH heating scheme challenging on MPEX. This scheme has not been demonstrated on Proto-MPEX at high density helicon mode, but it can be envisioned that a cavitylike structure must be used so that the X-mode wave reflects off the walls and crosses the 2nd harmonic cyclotron resonance multiple times. This scheme is envisioned as an alternative electron heating scheme using 105 GHz gyrotron frequency and 2nd harmonic cyclotron resonance at 1.875 T. The whistler wave heating requires fundamental cyclotron resonance heating using a ECH launcher from the high magnetic field side. This has previously been demonstrated on a linear magnetic mirror device [61], but has not been demonstrated on Proto-MPEX. To be conservative and maintain flexibility for these alternative heating schemes, the ECH region is designed to accommodate magnetic fields up to 2.5 T for fundamental electron cyclotron resonance whistler wave heating at 70 GHz as an alternative electron heating scheme.
Because some of these electron heating scenarios have low single pass absorption and because even previous O-X-B EBW experimental results indicate only approximately 20% of the available EBW power [62] is transported to the target, significant stray microwave power may end up at axial locations other than the desired target location on MPEX. Even small microwave power levels have been known to damage dielectric windows, diagnostics and other components on fusion experiments [63], so microwave absorbers have been deemed necessary for steady-state MPEX discharges to absorb the stray microwave power and prevent this power from leaking into other locations. These microwave absorber regions will be located adjacent to the ECH region and will be designed with materials that have high microwave absorption. A conceptual design for the microwave absorber is shown in [56].

MPEX ion temperature
As shown in figure 16, up to 30 kW of ICH heating on Proto-MPEX used here achieved a T i = 10 eV and did not achieve the source requirement of n e = 1 × 10 20 m −3 and T i = 30 eV for MPEX scenarios, so more ICH power is needed for MPEX. Similar to ECH heating, a linear extrapolation is done using plasma pressure as the metric given that ICH heating has also been observed to modify density as well as ion temperature. Magnetic flux expansion differences on Proto-MPEX were also taken into account. Unlike ECH, the ion temperature measurement is a line of sight chord measurement and there are indications the ion temperature profile may be hollow [31] so conservative considerations for the core ion temperature need to be taken into account. Based on the data in figure 16, density of approximately 1.5 × 10 19 m −3 , and these extrapolation considerations, the required ICH power is estimated to be between approximately 250 and 350 kW for a linear extrapolation to the desired plasma pressures on MPEX. 400 kW of ICH source power is conservatively planned. While this ICH power level is admittedly a large extrapolation, the experimental data and COMSOL modeling on Proto-MPEX suggests that the heat flux and ion temperature increase linearly with ICH power.
Based on the magnetic field requirement of 1 T at the target, magnetic field >1.25 T at the ECH location and that magnetic field at the ECH region > magnetic field at the ICH region >magnetic field at the target in 'downhill' operation, the magnetic field at the ICH location on MPEX is chosen to be 1.2 T for the launched high field side magnetic field and 1.1 T for the fundamental ion cyclotron resonance. The ICH modeling and experimental results on Proto-MPEX suggest the ICH antenna and ICH resonance magnetic fields should be somewhat close the fundamental ion cyclotron resonance to maximize antenna loading and core ion heating efficiency. On MPEX, the fundamental deuterium cyclotron resonance corresponds to a frequency of approximately 8.5 MHz at 1.1 T. ICH frequencies were chosen between 4 and 9 MHz on MPEX to provide some flexibility for the choice of magnetic field and to ensure fundamental ICH heating for both deuterium and helium discharges, which is of interest to PMI science. Similar to the electron heating region, a low neutral pressure is required in the ICH region. For ICH heating, this is due to charge exchange losses rather than electron neutral collisions. Charge exchange losses depends on the electron density, neutral gas density, ion temperature and charge exchange cross section. Assuming 100% deuterium plasmas, a central density of 4 × 10 19 m −3 and parabolic radial profile to the ICH antenna window, figure 20 shows estimated charge exchange neutral losses for Proto-MPEX and MPEX parameters as a function of neutral pressure and ion temperature. For ion temperatures of 10 eV and neutral pressure of 0.01 Pa such as on Proto-MPEX, the charge exchange losses are only a few kW. For ion temperatures expected up to 30 eV at the MPEX ICH location, a neutral pressure of ∼0.01 Pa is predicted to produce on the order of 10 kW of ICH power losses. Higher neutral pressures will lead to larger charge exchange neutral losses that will significantly reduce the efficiency of ICH heating on MPEX. Neutral pressures <0.01 Pa is therefore set as the requirement for the ICH region on MPEX. Because the PMI target region is expected to have a much higher neutral pressure in the range from 0.1 to 10 Pa depending on the MPEX scenario, skimmers are again required on MPEX to maintain differential pumping between the ICH and PMI region. Figure 17 shows that the total heat flux on MPEX is the sum of the individual contributions of helicon-only, ICH-only, and ECH-only power. Similar to the electron and ion temperature, an extrapolation is used here for the heat flux. A linear extrapolation from 90 kW helicon, 25 kW ICH, and 35 kW ECH on Proto-MPEX to 250 kW helicon, 400 kW ICH, and 400 kW ECH for MPEX will result in a core heat flux of approximately 20 kW m −2 . This extrapolation however does not take into account the different magnetic configuration for these experiments on Proto-MPEX and MPEX. In MPEX, the magnetic field will steadily drop in value axially from the location of wave absorption to the target. ICH and ECH heating have been observed to be strongly dependent on magnetic field on Proto-MPEX [45,49] This specific discharge shown in figure 17  was a proof of principle experiment and was not optimized for both ECH and ICH heating. Based on existing experimental data, the heat flux for MPEX is expected to about a factor of 1.3 higher at the target for optimized MPEX magnetic field at the ECH and ICH regions. The magnetic field on MPEX at the target is 1 T is also significantly higher than in than the Proto-MPEX target magnetic field (0.35 T) in figure 17. Due to magnetic flux expansion, the central heat flux is expected to increase another factor of √ 1/0.35 ∼ = 1.7. Taking into account the corrections mentioned above for the extrapolation, estimates indicate that 250 kW helicon, 400 kW ICH, and 400 kW ECH for MPEX will result in a core heat flux of approximately 40 MW m −2 . This is larger than the heat flux expected for all MPEX scenarios. Given the previous results where the helicon plasma source, electron heating, and ion heating can individually satisfy the required source n e , T e , and T i , the combined helicon + ECH + ICH results on Proto-MPEX suggest that MPEX can achieve all the MPEX scenarios for combined helicon + ECH + ICH operation.

Discussion and conclusion
In conclusion, this paper highlights recent Proto-MPEX experiments and Proto-MPEX and MPEX modeling activities. Using a mixture of experiments, physics-based modeling and extrapolation, the physical and technical basis results demonstrate that MPEX can achieve all the MPEX goal scenarios for fusion reactor-relevant divertor parameters ranging from sheath limited to conduction limited to partially detached to fully detached divertor regimes. The physical and technical basis further sets the functional requirements for the RF power, frequency, magnetic field, neutral pressure, and key in-vessel components in the helicon, ECH, ICH, and PMI regions.
From the magnetic field requirements set by the physical and technical basis, the baseline magnetic field profile on MPEX has been designed and is shown in figure 21 for the High n e MPEX scenario. Helicon mirror fields are clearly observed in the helicon region and minimal magnetic ripples are shown in ECH, ICH, and PMI regions. The magnetic field in ECH region > magnetic field in the ICH region > magnetic field in the PMI region. Fundamental ICH and 2nd harmonic ECH resonance locations are labeled.
A summary of the MPEX functional requirements such as magnetic field, RF net power, RF frequency, and neutral pressure in the helicon, ECH, ICH, and PMI regions are shown in table 4 to achieve the desired MPEX scenarios. A range of magnetic fields and frequencies are specified to account for different electron heating and ion heating options. The need for key in-vessel components such as skimmers and limiters in the helicon region, microwave absorbers in the ECH region, skimmers in the ICH region, and target in the PMI region are also highlighted in this paper. These functional requirements directly lead to the design of MPEX. Description of the conceptual design of the MPEX magnet systems are in [64], conceptual design of the in-vessel components is in [56], and conceptual design of the RF systems and the entire MPEX experiment are in [10]. A summary of the MPEX final design is in [65].