{"id":"eba77c81-8faf-4142-ba93-a752cdbbf503","arxiv_id":"2411.09232","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A Hermite-Laguerre spectral velocity-space formulation in GENE-X reproduces grid-based edge and scrape-off layer turbulence profiles for TCV-X21 with about a 50x cost reduction.","lead":"The paper replaces the velocity-space grid in the GENE-X gyrokinetic turbulence code with a Hermite-Laguerre spectral expansion and shows it reproduces edge and scrape-off layer turbulence profiles for the TCV-X21 tokamak case about 50 times faster than the grid version. It matters because high-fidelity edge turbulence simulations, previously too expensive for routine use, could become practical for medium-sized tokamaks and ultimately for reactor-relevant devices.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The low-resolution advantage depends on a single constant scaled temperature tau_alpha per species; for an edge/SOL temperature ratio like H-mode or ITER (T_edge/T_SOL > 10), Eq.","rationale":"I agree with the reader's weakest assumption. The constant-tau_alpha issue is not merely a tuning detail: it is a mathematical constraint in Eq. (C.7) that controls the exponential decay of the spectral coefficients. The paper demonstrates convergence only in a regime where T_alpha/tau_alpha is close to 1; Fig. 8 and the Dirichlet-boundary caveat make that explicit. In a more realistic reactor edge, the temperature range makes a single constant tau_alpha inadequate at the claimed low resolution. The MMS verification and the TCV-X21 profile comparisons are credible evidence for the specific case, so I would not reject the paper; the verdict stays CONDITIONAL. A secondary gap is that Sec. 7.3 measures the headline speed-up on a (6,4) run whose OMP profiles are not shown in Sec. 6.3, but that is a presentational gap and would not by itself overturn the case-specific claim.","tokens_in":27804,"tokens_out":8058,"duration_ms":90889,"concrete_test":"Take a representative H-mode/ITER-like initial profile with T_edge approximately 1 keV and T_SOL approximately 20 eV. Using Eq. (C.7), compute the smallest (Nvpar, Nmu) needed for local Maxwellians at both temperatures to decay by four orders of magnitude in coefficient amplitude. If this required Nvpar exceeds about 8 at Nmu=4 (the resolution used to claim the speed-up), the low-resolution advantage does not transfer. The same calculation for the TCV-X21 profile should reproduce the paper's (16,8) or better; comparing the two counts directly tests the scope of the speed-up claim.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that a Hermite-Laguerre spectral velocity-space basis gives a ~50x speed-up with (Nvpar,Nmu)=(6,4) rests on the existence of one constant scaled temperature tau_alpha per species. The paper chooses tau_e=114 eV and tau_i=102.5 eV by trial and error (Sec. 6.1) to satisfy Eq. (C.9). For a Maxwellian at temperature T_alpha, Eq. (C.7) gives coefficients scaling as (1 - T_alpha/tau_alpha)^(floor(p/2)+j); convergence requires T_alpha < 2 tau_alpha and is slow when T_alpha << tau_alpha. Fig. 8 shows the spectrum is indeed broad where T_alpha deviates from tau_alpha, and the paper itself attributes the far-SOL agreement to the Dirichlet boundary condition rather than to spectral convergence (Sec. 6.3, Fig. 12). For TCV-X21 the temperature ratio across the domain is modest, so tau_alpha approximately equal to T_edge works. For an H-mode pedestal or ITER-like case, T_edge/T_SOL can exceed 10; no constant tau_alpha can make both the hot edge (T_alpha close to 2 tau_alpha) and the cold SOL (T_alpha << tau_alpha) converge with Nvpar about 6-8 and Nmu about 4. Section 8 concedes that the required resolution will vary with temperature gradients and instability type. This is a scope limitation, not an internal inconsistency, but it is exactly the condition on which the headline 'enables high-fidelity simulations towards ITER' depends; the transferability of the speed-up is therefore the least secure part of the central claim.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript reports the first implementation of a velocity-space spectral (Hermite-Laguerre) discretization in the full-f gyrokinetic edge/SOL code GENE-X, replacing the grid discretization in v_parallel and mu. The authors derive the spectral form of the Vlasov-Maxwell system and the LBD collision operator, verify the implementation with the method of manufactured solutions in three geometries, and then apply the method to the TCV-X21 reference case. They compare outboard-midplane profiles of density, electron/ion temperature, and radial electric field against existing GENE-X grid results, and they report a speed-up of approximately 50 for a spectral resolution of (Nvpar,Nmu) = (6,4) relative to an optimized grid simulation with (80,24). The paper concludes that spectral acceleration enables high-fidelity edge/SOL gyrokinetic simulations on CPU-based machines within a few days and argues that this moves the method toward reactor-relevant devices.","tokens_in":28242,"tokens_out":6885,"duration_ms":79096,"significance":"If the central claim is correct, the paper is a substantial methodological contribution: it demonstrates that a full-f gyrokinetic edge/SOL code with X-point geometry can use a spectral velocity-space basis in place of a high-resolution grid, while preserving the physics of TEM-dominated turbulence and the kinetic collisional cooling of trapped electrons. The MMS verification in slab, circular, and toroidal geometries is a concrete strength, as is the use of openly archived grid data for comparison. The claimed order-of-magnitude reduction in velocity-space resolution and the factor-of-50 speed-up are significant for the feasibility of edge/SOL gyrokinetics on current CPU clusters. The paper is also honest about several limitations: the constant scaled temperature tau_alpha is chosen by trial and error, the far-SOL agreement is partly a boundary-condition artifact, and the required spectral resolution will vary with temperature gradients and instability type. Those caveats, however, mean that the headline transferability to ITER-like conditions is not established by the presented evidence.","major_comments":[{"comment":"The central claim of 'excellent agreement' with the grid simulations rests exclusively on visual profile comparisons. No quantitative error metric is reported for the OMP density, Te, Ti, or Er profiles, nor are the spectral and grid profiles compared against their respective standard deviations in a quantitative way. Please compute relative L2 or pointwise errors between the spectral and grid profiles over well-defined radial ranges (e.g., edge region, near-separatrix region, and far SOL), and report how these errors vary with spectral resolution. Without such a metric, the central claim of the abstract cannot be assessed independently of visual inspection.","section":"Sec. 6.3, Figs. 9-13"},{"comment":"The speed-up factor of approximately 50 is based on a spectral simulation with (Nvpar,Nmu) = (6,4), but the physics validation in Section 6 uses (4,2), (6,2), (8,4), and (16,8); no OMP profile or other physical observable is shown for (6,4). Since the speed-up is the paper's headline quantitative result, the (6,4) resolution must be demonstrated to reproduce the grid profiles with the same fidelity as the resolutions studied in Section 6. Please add the (6,4) case to the profile comparison at the stated Delta_RZ = 3.7 rho_ref, or otherwise justify that interpolating between (6,2) and (8,4) is sufficient.","section":"Sec. 7.3, Table 1"},{"comment":"The artificial Landau-damping-like sink, with coefficient K_parallel = 0.1, is stated to 'not affect the saturated turbulent state', but no sensitivity scan over K_parallel is presented. The damping term is applied precisely to the flux variables used at the low resolutions for which the speed-up is claimed, so a dependence of the saturated profiles or fluctuation level on K_parallel would directly affect the validity of the low-resolution results. Please include a K_parallel scan (at least at the resolutions used in the speed-up comparison) showing that time-averaged OMP profiles and ideally fluctuation amplitudes are unchanged.","section":"Sec. 4.3, Eq. (23)"},{"comment":"The transferability of the method to H-mode or ITER-like conditions is not supported by the present evidence. Equation (C.9) gives only a lower bound on tau_alpha, and the convergence of the expansion for a Maxwellian at temperature T_alpha depends on |1 - T_alpha/tau_alpha|. Figure 8 shows that the spectral coefficients decay slowly where T_alpha deviates from tau_alpha, and Section 8 concedes that the required resolution depends on temperature gradients. For a case with T_edge/T_SOL > 10, no single constant tau_alpha will simultaneously provide fast convergence at the hot edge and at the cold SOL with only 6-8 parallel and 4 perpendicular modes. The authors should either demonstrate the approach on a synthetic or real case with a larger temperature ratio, or explicitly restrict the claim to L-mode-like cases with moderate temperature variation and remove or soften the ITER statement from the abstract.","section":"Appendix C, Sec. 6.1, Sec. 8"},{"comment":"The configuration-space boundary conditions used for the spectral coefficients are described as 'not based on physical principles' (projected Maxwellian with initial profiles), and the text states that the far-SOL agreement in Ti is due to the Dirichlet boundary condition rather than physical dynamics. This means that part of the claimed agreement in the SOL is a boundary artifact, not a test of the spectral method. The paper should state explicitly over which radial range the spectral/grid comparison is considered physical, and should flag the same caveat for the density and Te profiles, not only for Ti.","section":"Sec. 4.5, Sec. 6.3"}],"minor_comments":[{"comment":"The CPU/node counts appear inconsistent for the (6,2) Marconi row: 32 nodes with 48 cores per node (A3 partition) gives 1536 CPUs, not 3072. Please verify all node/core counts and the resulting CPU-hour estimates.","section":"Table 1"},{"comment":"The time-averaging procedure is described as a 'toroidal and time average' over 0.1 ms, but the details are incomplete: specify how the toroidal average is performed over the Nphi = 32 poloidal planes, whether the interpolation to the OMP line precedes or follows the average, and how many instantaneous samples enter the time average.","section":"Sec. 6.3"},{"comment":"The sentence 'values of tau_alpha close to (but larger than) tau_alpha,c ensure a faster convergence in the SOL region but a slower convergence in the edge region' appears difficult to reconcile with Eq. (C.7): when T_alpha << tau_alpha, the factor (1 - T_alpha/tau_alpha) is near unity, which gives slow decay, not fast convergence. Please check the wording and clarify the qualitative behavior of the convergence as a function of T_alpha/tau_alpha.","section":"Appendix C"},{"comment":"The CFL estimate in Eq. (24) uses min(R) without defining the normalization or whether R is the major radius in the normalized units of Appendix A; please define all symbols in the equation.","section":"Sec. 4.4, Eq. (24)"},{"comment":"The collision operator is called the 'Lernard-Bernstein/Dougherty' operator; the correct spelling is Lenard-Bernstein. Please correct this typo.","section":"Sec. 2"},{"comment":"The description of the spectral stencil, including two-sided ghosts in p, one-sided ghosts in j, and edge ghosts for the magnetic-pumping terms, is terse. A few sentences clarifying how the truncation is applied and how ghost coefficients are set (zero? extrapolated?) would help the reader reproduce the implementation.","section":"Sec. 4.2, Fig. 1"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is a technically serious contribution from an established group, and the MMS verification plus the honest discussion of limitations are commendable. The main concern is that the headline claims ('excellent agreement', factor-of-50 speed-up, and the path toward ITER) are currently supported by visual comparisons, an unvalidated (6,4) resolution in the speed-up benchmark, and no K_parallel sensitivity study. These are fixable within the scope of the paper, so I do not recommend rejection; I recommend major revision to add the missing quantitative evidence and to temper the transferability claims accordingly."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Read this one if you want to know whether velocity-space spectral methods can make full-f edge/SOL gyrokinetics affordable. The headline result — (6,4) Hermite-Laguerre coefficients reproducing grid (80,24) OMP profiles for TCV-X21 at roughly 50x lower cost — is credible, and the paper is the first demonstration of this in an X-point full-f GK code. The derivation is careful, the MMS verification is clean second-order in all three geometries, and the resolution scans move toward the grid baseline. That is real evidence.\n\nWhat is genuinely new is the GENE-X implementation with X-points and the TEM-dominated TCV-X21 test. Hermite-Laguerre expansions are not new, and the authors say so. The credit goes to engineering the approach into a working FCI full-f code and showing it survives a case where trapped-electron physics is sensitive to velocity-space structure.\n\nThe soft spots are real but not load-bearing. The \"excellent agreement\" is asserted from plotted profiles; there is no quantitative error metric. The benchmark is their own grid GENE-X, so it is a consistency check, though the MMS verification and convergence scans reduce that concern. The K_parallel damping claim — that the saturated state is insensitive to it — is stated without a sensitivity scan, and no spectral data or code is released. All of these are addressable.\n\nThe larger caveat is the one the authors concede in Section 8: the low resolution works because a single constant scaled temperature tau_alpha per species can cover the temperature range. For TCV-X21, T_edge/T_SOL is modest, so tau_e = 114 eV and tau_i = 102.5 eV are adequate. For an H-mode pedestal or ITER, where the temperature ratio can exceed 10, no constant tau_alpha will keep both the hot edge and cold SOL converged at (6,4). The paper's own Fig. 8 shows the spectrum broadening where T deviates from tau_alpha, and Section 6.3 correctly says the far-SOL agreement is mostly the Dirichlet boundary condition, not physics. This makes the ~50x speed-up a case-specific result, not a demonstrated reactor-ready capability. The ITER sentence in the abstract overreaches relative to the evidence, but the paper itself is mostly honest about the scope.\n\nThis paper is for plasma physicists and computational scientists working on gyrokinetic boundary codes. It deserves a serious referee. If I were refereeing, I would ask for a quantitative profile-difference metric, a K_parallel sensitivity scan, and a clearer statement that the speed-up is demonstrated only for moderate temperature-ratio L-mode cases. The central methodological claim holds for what it actually tests.","headline":"A solid numerical-methods paper: the Hermite-Laguerre velocity-space implementation in GENE-X gives a credible ~50x speed-up for TCV-X21 and reproduces grid profiles, but the single-scale-temperature basis limits how far that speed-up transfers to steep H-mode or ITER cases.","tokens_in":28712,"tokens_out":2235,"would_cite":true,"duration_ms":25932,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["52.65.-y","52.35.Ra","52.25.Fi"],"model":"deepseek-v4-flash","headline":"A velocity-space trick speeds gyrokinetic edge turbulence runs 50x","keywords":["gyrokinetics","spectral velocity-space expansion","Hermite-Laguerre basis","edge and scrape-off layer turbulence","full-f gyrokinetic code","trapped electron modes","computational speed-up","method of manufactured solutions"],"falsifier":"A gyrokinetic simulation of a different edge/SOL scenario with a wider temperature range or a pronounced H-mode pedestal, run with the spectral approach at the claimed low resolution (e.g., $N_{v\\|} \\approx 6$, $N_\\mu \\approx 4$) and with the single-constant $\\tau_\\alpha$ recipe, would falsify the generality claim if its OMP profiles deviated systematically from grid or experimental results and if increasing the resolution into the range $N_{v\\|} \\approx 16$ or beyond failed to recover the grid result. More narrowly, a scan over the trial-and-error parameter $\\tau_\\alpha$ in TCV-X21 would falsify the robustness claim if small variations of $\\tau_\\alpha$ around the chosen values (114 eV, 102.5 eV) changed the computed OMP density or temperature profiles by more than the quoted agreement with the grid data.","tokens_in":27603,"feed_emoji":"⚡","tokens_out":4003,"duration_ms":37252,"temperature":0.7,"pith_summary":"The paper presents the first full-f gyrokinetic simulations of edge and scrape-off layer turbulence that accelerate the velocity-space discretization with a spectral (Hermite-Laguerre) expansion, implemented in the GENE-X code. The central claim is that this spectral formulation reproduces the outboard midplane profiles—density, electron and ion temperatures, and radial electric field—of the TCV-X21 reference case with excellent agreement against previously validated grid simulations, while requiring vastly fewer velocity-space degrees of freedom. The quantitative payoff claimed is a speed-up of approximately 50 for TCV-X21, reducing the cost from millions of CPU-hours and weeks of wall time to about 0.05–0.1 MCPUh and one to two days on CPU-based supercomputers. If correct, this would make routine high-fidelity gyrokinetic edge/SOL studies feasible for medium-sized devices and move reactor-relevant devices such as ITER within reach of this modeling approach.","feed_headline":"A velocity-space trick speeds gyrokinetic edge turbulence runs 50x","feed_subtitle":"Hermite-Laguerre spectral expansion reproduces TCV-X21 profiles and cuts the cost by two orders of magnitude, the paper reports.","key_machinery":"The central object is the spectral expansion of the full-f distribution function onto scaled Hermite-Laguerre polynomials, $F_\\alpha = \\sum_{p,j} N^{pj}_\\alpha \\hat H_p(\\hat v_{\\|\\alpha}) L_j(\\hat\\mu_\\alpha) F_{M\\alpha}$, with a constant per-species scaled temperature $\\tau_\\alpha$ chosen a priori ($\\tau_e = 114$ eV, $\\tau_i = 102.5$ eV for TCV-X21). The Hermite-Laguerre basis carries the argument: it converts the 2D velocity-space grid into a small set of coupled spectral coefficients, with the coupling expressed through sparse recurrence identities (Eq. 15). The spectral formulation yields closed expressions for the GK Vlasov equation (Eq. 12), the quasineutrality, Ampere, and Ohm equations (Eq. 16), and the LBD collision operator (Eq. 17), with the fluid moments of interest expressed directly in terms of low-order coefficients (Eq. 21). The spectral approach also exactly conserves the total energy of the GK system, and a Landau-damping-like diagonal dissipation term is added at the highest orders to stabilize the truncation.","core_discovery":"The paper claims that a velocity-space spectral formulation based on scaled Hermite-Laguerre polynomials can replace the grid discretization in the full-f gyrokinetic code GENE-X without loss of fidelity for edge and SOL turbulence, at a fraction of the computational cost. The authors state that the spectral approach reproduces the OMP profiles of density, temperature, and radial electric field of the TCV-X21 case—turbulence dominated by trapped electron modes—with excellent agreement and significantly lower velocity-space resolution, and that a speed-up of approximately 50 is achieved for that case. They further argue that the spectral discretization is particularly advantageous at high collisionality, because the LBD collision operator has a sparse spectral representation and its CFL constraint scales linearly rather than quadratically with resolution.","pith_inferences":["The approximately 50x speed-up and the low-resolution fidelity are demonstrated for a single scenario (TCV-X21) with a particular temperature profile; the extrapolation to other devices relies on the assumption that a single constant $\\tau_\\alpha$ can be found that resolves the temperature range, which may be more difficult for H-mode pedestals or detached/divertor scenarios with wider temperature","The spectral formulation's advantage is expected to be larger at high collisionality, because collisions damp the higher-order spectral coefficients and accelerate convergence; the collisionless limit requires higher spectral resolution, as the paper itself shows for TCV-X21.","The success of the approach for TEM-dominated turbulence suggests that the Hermite-Laguerre basis (which is well-suited to drift-kinetic and collisional dynamics) may also perform well for other drift-wave instabilities, but its performance for strongly electromagnetic or kinetic-ballooning regimes, where fine velocity-space structure matters, remains an open question the paper does not address.","The Dirichlet boundary conditions that set flux variables to zero and pin the distribution at the boundary to a local Maxwellian are acknowledged to be non-physical; improving them (e.g., with sheath boundary conditions) could change the far-SOL predictions, where the paper attributes the agreement to the boundary condition rather than to the physics."],"forward_implications":["A spectral resolution of about $(N_{v\\|}, N_\\mu) \\approx (6,4)$ suffices to reproduce the grid simulation results for TCV-X21, compared to (80, 24) for the optimized grid case, reducing the velocity-space degrees of freedom by roughly two orders of magnitude.","TCV-X21-class L-mode edge/SOL gyrokinetic simulations can be completed within a few days (about 0.05–0.1 MCPUh) on current CPU-based supercomputers, versus several million CPU-hours and several weeks for the grid approach.","The spectral approach captures the key kinetic mechanism of the TCV-X21 validation—the collisional cooling of trapped electrons—and reproduces the electron temperature OMP profile without resolving the fine structure of the trapped-passing boundary.","The approach is claimed to extend to larger devices: the authors hypothesize that a similar spectral resolution is adequate for L-mode scenarios in ASDEX Upgrade-class machines, though they note the required resolution likely depends on temperature gradients and instabilities.","The spectral formulation exactly conserves the total energy of the GK Vlasov-Maxwell system, providing a global energy-consistency guarantee that is demonstrated analytically in the paper."],"supporting_citations":[{"why":"The grid-based GENE-X simulations of TCV-X21 that the spectral results are compared against and from which the OMP profiles are taken.","marker":"[25]"},{"why":"Defines the TCV-X21 reference case (L-mode discharge, magnetic configuration, experimental measurements) used as the validation scenario.","marker":"[26]"},{"why":"The GENE-X code and its grid velocity-space implementation and FCI configuration-space discretization, which the spectral approach builds upon.","marker":"[18]"},{"why":"The conservative multi-species LBD collision operator in GENE-X, whose spectral representation is derived and used.","marker":"[31]"},{"why":"The moment-based Hermite-Laguerre approach to gyrokinetics, which motivates and informs the spectral expansion used here and its convergence properties.","marker":"[28]"},{"why":"The method of manufactured solutions, used to verify the numerical implementation of the spectral formulation.","marker":"[27]"},{"why":"The optimized grid simulation with an equidistant v-perp grid that is used for the speed-up comparison and provides the grid data for the radial electric field profile.","marker":"[47]"}],"fun_headline_variants":["Velocity-space spectral trick gives 50x speed-up in edge turbulence runs","Hermite-Laguerre expansion accelerates gyrokinetic edge simulations 50-fold","Spectral velocity grid cuts edge gyrokinetic turbulence cost by 50x","GENE-X spectral method reproduces TCV-X21 profiles at 50x lower cost","Spectral velocity-space discretization speeds edge turbulence simulations 50x"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The spectral convergence and the claimed low-resolution fidelity rely on the existence of a single constant scaled temperature per species, chosen by trial and error, such that the Hermite-Laguerre basis is wide enough to represent the whole temperature range across the edge and scrape-off layer; if no such constant exists for a different scenario, the spectral resolution and speed-up will not transfer.","fun_headline_variants_meta":{"raw":{"variants":["Velocity-space spectral trick gives 50x speed-up in edge turbulence runs","Hermite-Laguerre expansion accelerates gyrokinetic edge simulations 50-fold","Spectral velocity grid cuts edge gyrokinetic turbulence cost by 50x","GENE-X spectral method reproduces TCV-X21 profiles at 50x lower cost","Spectral velocity-space discretization speeds edge turbulence simulations 50x"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000219,"raw_usage":{"total_tokens":1450,"prompt_tokens":960,"completion_tokens":490,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":576,"completion_tokens_details":{"reasoning_tokens":386}},"tokens_in":576,"tokens_out":490,"duration_ms":5880,"temperature":1.0,"reasoning_tokens":386,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T20:53:46.966293+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A gyrokinetic simulation of a different edge/SOL scenario with a wider temperature range or a pronounced H-mode pedestal, run with the spectral approach at the claimed low resolution (e.g., $N_{v\\|} \\approx 6$, $N_\\mu \\approx 4$) and with the single-constant $\\tau_\\alpha$ recipe, would falsify the generality claim if its OMP profiles deviated systematically from grid or experimental results and if increasing the resolution into the range $N_{v\\|} \\approx 16$ or beyond failed to recover the grid result. More narrowly, a scan over the trial-and-error parameter $\\tau_\\alpha$ in TCV-X21 would falsify the robustness claim if small variations of $\\tau_\\alpha$ around the chosen values (114 eV, 102.5 eV) changed the computed OMP density or temperature profiles by more than the quoted agreement with the grid data.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The grid-based GENE-X simulations of TCV-X21 that the spectral results are compared against and from which the OMP profiles are taken."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines the TCV-X21 reference case (L-mode discharge, magnetic configuration, experimental measurements) used as the validation scenario."},{"cited_title":"Michels, A","cited_arxiv_id":null,"evidence_quote":"The GENE-X code and its grid velocity-space implementation and FCI configuration-space discretization, which the spectral approach builds upon."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The conservative multi-species LBD collision operator in GENE-X, whose spectral representation is derived and used."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The moment-based Hermite-Laguerre approach to gyrokinetics, which motivates and informs the spectral expansion used here and its convergence properties."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The method of manufactured solutions, used to verify the numerical implementation of the spectral formulation."},{"cited_title":"Ulbl, Collision models for gyrokinetic simulations of edge turbulence in fusion plasmas, Ph.D","cited_arxiv_id":null,"evidence_quote":"The optimized grid simulation with an equidistant v-perp grid that is used for the speed-up comparison and provides the grid data for the radial electric field profile."}],"review_version":1}