PFPO plasma scenarios for exploration of long pulse operation in ITER

Long Pulse Scenarios (LPS) in ITER foreseen during the Pre-Fusion Power Operation (PFPO) phase of the ITER Research Plan (IRP) are assessed using 1.5D transport simulations within the ASTRA framework. Such assessment is required to predict the operational space for LPS operation in PFPO, as well as to evaluate which physics processes for LPS operation during Fusion Power Operation (FPO) could be studied during PFPO. An important aspect in the development of LPSs in PFPO is to minimize lifetime consumption of the Central Solenoid (CS) for these scenarios. The maximum pulse length achievable for LPSs in PFPO with no consumption of CS lifetime (currents in CS coils ⩽30 kA per turn) has been assessed for a range of heating schemes and heating mixes, confinement regimes (L-mode and H-mode) and for helium and hydrogen plasmas. The operational space of LPS and pulse length has been explored through density scans with the Heating and Current Drive mix required for the FPO Q ⩾ 5 steady-state plasma scenario (namely Neutral Beam Injection and Electron Cyclotron Heating) including acceptable shine through losses on the first wall for both helium and hydrogen plasmas. Fast particle physics aspects that are common between FPO plasmas and LPS PFPO H-mode plasmas at low densities are studied including MHD stability analysis with the KINX code and non-perturbative critical gradient model based on high-n Toroidal Alfven Eigenmodes (TAE) stability kinetic ballooning code HINST calculations.


Introduction
ITER operation in the hydrogen and helium plasmas has already been addressed in a series of recent papers, such as [1][2][3][4][5][6], etc. These papers assessed the operational space and discussed the H-mode operational space in PFPO taking into account the unfavorable isotopic dependence of the L-H power threshold and realistic plasma parameters as well as description of the Heating and Current Drive (H&CD) systems designed for ITER.
The focus of our present studies is the analyses of the possibility of Long Pulse Scenarios (LPSs) in the Pre-Fusion Power Operation (PFPO) phase of the ITER Research Plan (IRP) with the objective of exploring relevant physics for Fusion Power Operation (FPO) DT plasma operation in similar plasma conditions. FPO DT long plasma scenarios have been described in a series of studies (e.g. [7,8]) and the results in such studies will be used to put in context the PFPO LPOs but will not be further studied here since this is beyond the scope of the present. An important issue for PFPO is to minimize the consumption of the Central Solenoid (CS) fatigue lifetime since it is important that lifetime consumption of the magnet system is kept at very low levels before the start of FPO to ensure that ITER can achieve its neutron fluence goal of 0.3 MWa m −2 [9].
As mentioned above LPS (>1000 s) [7] and Steady-State Operation (SSO) with fully non-inductive driven current [8] are foreseen in the IRP [10] for the FPO phase demonstration of the Q ⩾ 5 fusion power goal and to maximize neutron fluence on ITER components; these scenarios are also attractive for future fusion reactor operation.
It has been shown [7,11,12] that LPS operation at FPO is possible with low normalized densities at high plasma currents, (i.e. low safety factor, q 95 ∼ BI −1 p ∼ 3) with conventional H-mode confinement or at higher normalized densities and lower currents with higher than H-mode confinement. In ITER, energy confinement is expected to degrade with reduction of plasma current as seen in present experiments [13], τ E ∼ τ Hy2,98 ∼ I p . Thus, LPS and SSO with reduced currents (q 95 > 3.5 − 4.5) as foreseen in ITER for Q ⩾ 5 operation, would require confinement better than the regular H-mode operation, H y2,98 = τ E /τ Hy2,98 > 1.2 − 1.5.
Both the high and low current versions of LPSs and the SSO foreseen for the ITER FPO phase have some common features. In particular: • available at: margin above the L-H power threshold (for densities higher than the Neutral Beam Injection (NBI) shine-through limit density) in the initial phases before alpha heating builds up, P aux /P LH,min < 2; • high fast particle pressure, β fast /β th > 0.1; • super-Alfvenic speed of fast particles (at least at high density, V fast /V A > 1); • toroidal rotation higher than in the 15 MA baseline scenario, caused by better confinement or lower density, V tor (0) > 200 km s −1 , with moderate Mach number for the fuel ions (high rotation speed but with a low Mach number), available at: <0.25; • low or Weak Reversed Shear (WRS) q profile configuration with q min ∼ 1; • relatively high density at the separatrix, n ped /n s < 4; • high pedestal pressure at low density predicted by the EPED1 + SOLPS scaling based on the Peeling-Ballooning limit [7].
Note that several of these features are inherent to all H-mode discharges at FPO where a low density and full auxiliary power are required for transition from the L-to H-mode when alpha heating is still small (see [14]). Long-pulse operation is desirable in PFPO-2 (and even in PFPO-1, if time permits) for a range of reasons. A very important one is to commission all plant systems to the duration required for FPO as well as to identify key operational and physics issues that will be encountered when operating long pulses in PFPO. This includes the use of magnetic sensors for plasma control and the operation of H&CD systems over long periods to demonstrate the capabilities of the H&CD systems to provide current drive efficiency as well as power deposition in the plasma with acceptable shine-through loads over long timescales.
The IRP explicitly includes two basic scenarios for longpulse operation in PFPO-2, both at 2.65/7.5 T MA −1 . However, this does not exclude others, some of which could already be explored in PFPO-1 if time allows. The first is a hydrogen L-mode scenario at 2.65/7.5 T MA −1 with reduced NBI energy/power and Electron Cyclotron Heating (ECH) for studies of erosion/re-deposition and fuel retention and a flattop length of ∼100 s. The second is an H-mode scenario (in hydrogen or helium) at 2.65/7.5 T MA −1 , with 33 MW of NBI and 20-40 MW of ECH and Ion Cyclotron Heating (ICH), having a maximum potential flattop length of ∼1000 s. The use of H&CD schemes for specific plasma conditions in PFPO is determined by the availability of the H&CD systems (only ECH is available in PFPO-1) as well as by shine-through loads of NBI [14], ECH [3,6] and ICH absorption and coupling [3], which restrict the range of plasma conditions in which they can be used.
To preserve CS fatigue lifetime for FPO it is important that for LPSs in PFPO the current in the CS remains under 30 kA per turn since, at this current level, no CS lifetime is consumed by long pulse operation. Studies of the magnetic flux provided by the CS in the context of ITER scenarios were described in previous studies [1,2].
The length of the current flattop, ∆t FT = ∆Ψ FT /U loop increases with the increase of the magnetic flux swing available for the current flattop, ∆Ψ FT , and decrease of the loop voltage, U loop ∼ (I p − I NI ) /σ. The plasma conductivity increases with temperature, σ ∼ T 3/2 e , which increases with heating power level. The non-inductive current in the plasma, I NI = I BS + I CD , consists of bootstrap current, I BS ∼ nT/I p , and current driven externally, I CD ∼ T 3/2 e P CD , both of which increase with heating power levels.
A study of the scenarios to be explored in PFPO with potential for LPS with low CS lifetime consumption and the assessment of the issues they allow to explore in the context of the IRP in PFPO and FPO operation is described in this paper.
The models used in the simulations of these plasma scenarios are described in section 2. Scaling formulae for the maximum duration of plasma current flattop for different limits on currents in the CS coils are derived in section 3 from existing full scenario simulations with plasma magnetic control. The physics aspects that can be studied with the LPSs identified for PFPO, in particular in the context of FPO operation, are described in section 4. An assessment of different aspects of plasma stability in key LPSs in PFPO is described in section 5. Section 6 is dedicated to discussion and conclusions.

Plasma models
To assess the ITER plasma parameters we model particle densities, temperatures, toroidal rotation and current density profiles, n e , T i , T e , V tor , j with 1D transport and 2D equilibrium performed with free boundary DINA [15] and fixed boundary ASTRA [16] solvers (i.e. 1.5D transport simulations). ASTRA simulations are carried out for the current flattop phase only with fixed boundary equilibrium calculated by DINA and applying the boundary conditions predicted by SOLPS parameterization [17]. For H-mode plasma conditions the heat diffusivities, χ i = χ e , are fitted at the Edge Transport Barrier to provide the value of the pedestal pressure, p e,ped , predicted by the EPED1 +SOLPS scaling [7]. In the ASTRA simulations for the H-mode phase we considered the GLF23 transport model with modified torque transport [18], as well as a more conservative Scaling Based Model (SBM). In the SBM, , we fit C χ , to provide the energy confinement expected in H-mode plasmas according to the H y2,98 scaling, τ E = τ Hy2,98 [13], in the Ohmic phase by Ohmic scaling [19] and in L-mode by the scaling in [20]. Particle diffusivity, D e = 0.2 χ. The spatial variable X is the square root of the normalized toroidal magnetic flux. The pinch velocity is fitted to provide the density peaking predicted by GLF23.
The plasma fuelling rate is adjusted to provide plasmas with the required density level. We note that, for L-mode and H-mode plasmas in PFPO, half of the Greenwald density, n e ≈ 0.5 n G , with is a typical value [10]. Concentrations of impurities, C imp = n imp /n e , are prescribed to control the NBI shine-through as well as ICH absorption for the three-ion scheme [4]. The main ion (hydrogen or helium) densities, n H or n He , are calculated from quasineutrality conditions, n e = ∑ i Z i n i . The rotation in the core is simulated including the torque source from NBI and with toroidal momentum diffusivity, χ ϕ = Prχ i , Pr = 0.3 [21]. In the pedestal, χ ϕ is fitted to provide the toroidal momentum confinement time proportional to the energy confinement time, τ ϕ ∼ τ E (τ E /2 < τ ϕ < 2 τ E ) which is a typical range foreseen for ITER from present experiments [21].
Two maximum ECH power levels have been considered: the baseline power level, P ECH = 20 MW, and higher level, P ECH = 30 MW, which is being studied as a possible early upgrade to the baseline. Hydrogen NBI (H 0 -NBI) is modeled following [8,22] with a combination of 16.5 MW on-axis and 16.5 MW off-axis NBIs, with maximum energy of H 0 , E p = 870 keV. ICH with a power up to P ICH = 20 MW, and range of frequencies, f IC = 40 − 55 MHz is modeled consistently with the presence of fast hydrogen from NBI by the TORIC-SSFPQL suite of codes [23].
The poloidal flux evolution was simulated taking into account bootstrap current and currents driven by NBI and ECH. Sawteeth are modeled by mixing of plasma parameters and fast ion redistribution within the Kadomtsev-like radial area connected with the q = 1 resonance surface position, X ST = 1.4 X(q = 1) and for Toroidal Alfven Eigenmodes (TAE) within the radius affected by TAE, which appears to be close to X ST .

Assessment of poloidal magnetic flux consumption
The poloidal magnetic flux, ∆Ψ FT , depends on the premagnetization of the CS (currents in the CS coils at the start of CS discharge), the flux consumption during the current ramp-up phase and the maximum allowable current in the two CS coils connected in series (CS1), which have the highest current.
Plasma operation with maximum current in the CS coils of ≲30 kA (per turn) allows an unlimited number of discharges in ITER, from the point of view of the CS fatigue lifetime. Therefore, we assess the maximum duration of plasma current flattop in the PFPO scenarios, when the CS discharge starts with initial currents in the coils of ∼ +30 kA, and the end of plasma current flattop-EOF, when the current in the CS1 coils hits the limit −28 kA (keeping a 2 kA margin for the plasma control actions at the start of plasma termination) on the basis of existing plasma magnetic control simulations. We first analyze the results of DINA simulations of two PFPO scenarios with q 95 ≈ 3 having different values of the I p at flattop and B t to determine the flux consumption balance in ITER and how to parameterize it. These are Scenario 1 with I p = 5 MA and B t = 1.8 T in He in H-mode operation, and Scenario 2 with I p = 7.5 MA and B t = 2.65 T in H in L-mode operation. The plasma current ramp-up in these scenarios starts after gas breakdown (BD), when the magnetic flux produced in the plasma by the currents flowing in the coils (CS and PF) and in the conducting structures, ⟨Ψ (BD)⟩ is about 79 Wb. Here we used the following definition of the magnetic flux linked with the plasma: where j is the plasma current density, Ψ ex (r, z) is the value of poloidal magnetic flux produced by the external currents (flowing in the coils and conducting structures) at the point with coordinates (r, z), and the integration is performed over the plasma cross-sectional area, S.
During the I p ramp-up, the variation of ⟨Ψ ⟩ compensates inductive and resistive losses of the magnetic flux, and the value of ⟨Ψ ⟩ at the Start Of Current Flattop (SOF) is: The inductive losses of ⟨Ψ ⟩ during the plasma current ramp-up, ∆Ψ ind (BD → SOF), can be expressed via the plasma inductance L: Here W is plasma magnetic energy, B p (r, z) and Ψ p (r, z) are the values of poloidal magnetic field and its flux produced by the plasma current at the point with coordinates (r, z). The first integration is performed over S, and the second (volume) integration is performed over the whole space.
The resistive losses of ⟨Ψ ⟩ during the plasma current rampup, ∆Ψ res (BD → SOF), can be expressed via the plasma loop voltage, U loop : Here j ohm , j bs and j cd are the respectively the current densities due to the Ohmic, bootstrap and auxiliary heating drive and σ is the plasma electrical conductivity. The integration is performed over the plasma volume V. The resistive losses can be also expressed via the 'Ejima coefficient', defined as L can be represented as follows: where W ex is the energy of the magnetic field, B p , produced by the plasma current outside the plasma and W in is the energy of this magnetic field inside the plasma: The value of L in can be written as: where the parameter l i is the so-called 'l i (3)'.
Using (6) and (7) the value of L ex can be expressed as Using the values of L (SOF), L (EOF) and l i (SOF), l i (EOF) in DINA simulations of Scenarios 1 and 2, we can conclude that the value of L ex during the current flattop has approximately a constant value: Taking into account (1), (2), (5) and (8), we can get the value of ⟨Ψ ⟩ at the SOF: Using (9), we obtain from (10) for R = 6.2 m: For the scenarios of plasma current ramp-up considered, the values of l i (SOF) and C E (SOF) are as follows.
For scenario 1 with dI dt ≈ 0.26MAs −1 , I (XPF) ≈ 3.1MA, P ECH = 0: Here P ECH is the power of ECH during current ramp-up after the X-point formation.
In Scenarios 1 and 2, the magnetic flux ⟨Ψ ⟩ depends approximately linearly on the current flowing in the two central CS coils (CS1), I CS1 . This is illustrated in figure 1(a). The discharge starts at I CS1 = +30 kA and the plasma current flattop finishes (EOF) at I CS1 = −28 kA. However, the precise value of ⟨Ψ ⟩ at the EOF depends on the waveforms of currents in the other CS coils (CS3U, CS2U, CS2L, CS3L), which are significantly different in scenarios 1 and 2, as shown in figure 1(b).
For the assessment of ∆t FT in scenarios with the maximum current in CS coils 30 kA, we will assume ⟨Ψ (EOF)⟩ ≈ −79 Wb. The value of ⟨Ψ (EOF)⟩ can be also expressed via the inductive and resistive losses of the magnetic flux during the plasma current flattop: Here: and where U loop is defined in (4).
Using (10)- (14), we obtain the equation for the assessment of the maximum duration of plasma current flattop, ∆t FT : As an example, figure 2 shows variation of l i in scenarios 1 (H-mode) and 2 (L-mode) in two time intervals [0, 800 s] and [0, 100 s]. The value of l i (EOF) in these scenarios are 0.76 in scenario 1 and 0.96 in scenario 2.
The values of l i (SOF) and C E (SOF) for scenarios 1 and 2, formula (15) can be approximately written as: (16) which will be used for our assessment of ∆t FT in scenarios with maximum current in the CS coils I CS ⩽ 30 kA allowing an unlimited number of discharges from the point of view of the CS operation lifetime. Note, that equation (16) provides a good approximation for the flux available for the current flattop at I CS ⩽ 30 kA in spite of the difference in the main ion species and heating during the current ramp-up phase. In further simulations, we use formula (16) to calculate the flattop length with the loop voltage from transport modeling as described in the following section.
Note, that approximate expressions similar to equation (16) can be derived for the case when the CS discharge starts with initial current in the coils of +20 kA, ∆Ψ FT,20 ≈ 100 − 16I p , as well as for full pre-magnetization, ∆Ψ FT,full ≈ 240 − 14I p . The flattop length for scenarios at full pre-magnetization modeled in [1,2] can be rescaled to the initial CS premagnetization levels of 20 and 30 kA using the analytic expression: This analysis shows that hydrogen discharges in L-mode can already provide a significant pulse length for 30 kA premagnetization in PFPO and thus no significant CS lifetime consumption (see figure 3(b)). In particular, for 5 MA plasmas with 20 MW of wave heating, flattop lengths are in the range 200-700 s, depending on the value of the plasma density (n e /n G = 0.2-1.0). These L-mode plasmas would be a natural extension of the commissioning activities at 1.8-2.65 T in PFPO-1 (for ECH) and PFPO-2 (for ICH and ECH) if the reliability of the ECH and ICH systems is sufficient to  attempt this long-pulse operation at this stage. As mentioned before, such long L-mode pulses could be used to commission control systems over long timescales, but would also offer a valuable tool for the study, comparatively early on in the Research Plan, to study erosion/deposition and fuel retention given the accumulated fluence on PFCs over these long pulse lengths.
In the next section, we discuss in more detail H-mode scenarios with long pulse lengths in PFPO since these provide additional possibilities to assess physics processes taking place in LPSs and SSO scenarios in FPO.

Similarity of H-mode LPS in PFPO and LPS and SSO in FPO
Let us first consider in more details the PFPO H-mode LPS which could be used for projection of the FPO. In particular, such LPS is predicted to be possible in half-field operation in hydrogen plasmas with NBI and ECH, i.e. the H&CD mix assumed for FPO SSO [8].
For half-field operation in hydrogen the ICRH absorption is not efficient in ITER. To keep acceptable NBI shine-through loads at full energy, full power H-NBI (E NBI = 870 keV, P NBI = 33 MW) we use plasma seeding by Neon [14]. To avoid shine-through of the EC waves we considered X-mode ECRH at B t = 2.65 T [6] which can lead to off-axis deposition when the temperature of the outer part of the core plasma is high due higher harmonic absorption as a consequence of Doppler effects. Global plasma parameters from the 1.5D transport modeling are presented in figure 4.
For one-third field operation, B t = 1.8 T, the NBI shinethrough loads are kept below the limits by reduction of the H 0 -NBI energy to E NBI = 540 keV with the resulting reduction of the NBI power to P NBI = 10 MW. Note, that such a reduction of energy makes the ratio of the velocity of the fast ions to the Alfvén velocity closer to that of DT full field operation for the same densities normalized to Greenwald [24], V NBI /V A ∼ 1 . In these scenarios, in addition to NBI, we consider 20-30 MW of ECH. For ECCD we assume the same scheme of the power distribution between launchers as for SS FPO [8]. We note that for 1.8 T operation, ECH operates in third harmonic which has the specific issues in the transient phase to access H-mode discussed in [3].
It is interesting to note that the GLF23 transport model predicts plasma profiles and global parameters for PFPO close to SBM predictions (see figures 4-6), tables 1 and 2. In particular, the H-factor, predicted by GLF23 is, H y2,98 ∼ 1.1. The largest difference is predicted for toroidal rotation because of the assumption of the reduced GLF23 model, χ ϕ = Prχ i , and the high ion thermal diffusivity near the plasma center predicted for such plasma conditions. Note that to avoid use of ECH power for half-field operation in X-mode leads to peripheral deposition being significant [6]. Nevertheless, both models predict rather peaked temperature profiles (see figure 6) due to NBI heating.
In PFPO-2, the IRP also considers two scenarios for full power operation with P aux = 73 MW, P NBI = 33 MW, P ECH = 20 MW, P ICH = 20 MW in plasmas with mixed helium and hydrogen. These are the 3-ion ICH heating scheme at B t /I p = 3.13/8.8 T MA −1 (see [4,24]), and the helium plasma with hydrogen minority heating scheme at B t /I p = 2.65 T/7.5 MA (see [24,25]). The results of 1.5D transport simulations of the 3-ion and hydrogen minority scheme with dominant hydrogen fuelling, C H ∼ 66%, and C He ∼ 10%, as well as hydrogen minority ICH heating scheme with dominant He fuelling, C H ∼ 6%, and C He ∼ 40% with scaling based transport model are presented in figures 7, 10(e), (f ), and table 1, case 3.
Note, that for the case of 3-ion heating some Ne (C Ne ∼ 0.01) is required to keep NBI shine-through loads at an acceptable level, requiring that the He 4 fraction be adjusted properly to maintain an efficient 3-ion heating. Combining conditions for absorption in the presence of beryllium (Be) [24] and ions with Z/A =1/2 ( 4 He, 10 Ne) [26] one gets the following expression for the concentration of helium, C 4He : 6(C 4He = 5C Ne ) = 10C Be ⩽ 1.
For C Ne = C Be = 0.01, this yields C 4He ⩽ 0.1. For such a scenario SBM for n/n G = 0.5 predicts long pulse operation at ∆t FT30 = 530 s, with rather high fraction of fast ions, W f /W tot = 0.13, and some margin for H-mode operation P SOL /P LH = 1.24.
The normalized power deposition distribution for the PFPO cases discussed above is displayed in figure 8. In the whole set of cases considered here the predicted plasma temperature peaking, T e,0 /T e,ped varies in the range from 2 to 4.
Full power operation in helium plasma with ICH hydrogen minority heating at frequency f ICH ∼ 40 MHz is predicted to have the most peaked power deposition (see Pn,HeH in      More peaked T e can be reached by aiming of P ECHEL closer to the center in 1.8 T plasmas [5]. Note, that in spite of the difference of the power deposition profiles (figure 8) the predicted temperature profiles remain rather peaked (figures 5-7). We now compare the PFPO LPS considered above with the FPO plasmas in a similar density range to identify common physics features and thus what can be learnt from PFPO LPS towards FPO. We note that a low density plasma phase at sufficiently high auxiliary heating power, P aux ∼ P aux,Baseline , will be required for the baseline scenario (B t /I p = 5.3 T/15 MA) to enable the transition from L-to H-mode, P sol = P α + P aux -P rad > P L-H (n e ) and then to build up the alpha heating level up to Q = 5 to sustain the H-mode plasma, following which the density can be increased further towards the achievement of Q = 10 [27]. This Q = 10 access strategy in ITER follows from the density dependence of the alpha-heating, P α ∼ n D n T ∼ n 2 e , and unfavorable density dependence of the L-H power threshold, P L-H ∼ n ν e , with ν ∼ 0.7-1 [28,29] (above some critical density [30], n e > n L-H,crit ∼ 0.35 n G for ITER at q ∼ 3). Such densities for 15 MA baseline DT scenario, n e ∼ 4-5 × 10 19 m −3 , are similar to those for one-half, one-third magnetic field operation, at the densities required for H-mode in the PFPO phase (typically n e ∼ 0.4-0.6 n G ). We note that while low density operation at 5.3 T/15 MA in DT can provide long pulse capability in FPO for Q = 3-5 (see figure 9(a) and [7], there are two other ITER reference DT LPSs for Q ⩾ 5 that can be considered in this comparison between PFPO LPSs and FPO, namely the H y2,98 = 1.25, hybrid-LPS with B t /I p = 5.3 T/12.5 MA [31], and the steadystate scenario [8,32], which requires H y2,98 > 1.5. The results of 1.5D transport simulations for DT operation for such scenarios are shown in figures 9 and 10 including comparison with PFPO LPS.
Comparison of the global parameters of the PFPO and FPO LPSs reveals may similarities as seen in figures 9 and 10, especially in the low density phase to access high Q in the reference FPO scenarios. For these FPO scenario phases (see figures 9, 10 and tables 1, 2) the PFPO LPSs have similar high fraction of the fast ion pressure, high toroidal rotation, weak and reversed magnetic shear, normalized pressure, high fraction of driven and non-inductive current, which will allow the study of the associated physics effects already in PFPO. Since many of such features are commonly associated with enhanced H-mode confinement in present experiments, and foreseen in ITER for long pulse operation in DT with Q ⩾ 5, PFPO LPSs may already provide an early indication of enhanced H-mode confinement in ITER and which specific physics feature may contribute most to it.
The impact of common PFPO and FPO local stability features for the scenarios modeled above is discussed in the following section since PFPO plasmas could be used to study fast particle effects before FPO since the high fast particle densities expected in DT may impact plasma transport, effectiveness of alpha heating and fast particle loads to the wall.

Stability and fast particle analyses
The results of the MHD stability analysis by KINX code [33] during the current profile evolution between sawteeth are presented in figure 11 specifically for 2.65 T/7.5 MA hydrogen H-modes, but it is typical of all PFPO H-mode long pulse cases considered in our studies. The n = 1 infernal/external kink mode stability beta-limit evolves between the sawteeth depending of the proximity of safety factor minimum, q min , to q = 1, resulting in sawtooth mixing. The other modes remain far from ITER-wall (weak wall stabilization for all n's) stability limits once q min > 1. Note that such evolution is found to be similar in all low-density DT LPS FPO and hydrogen PFPO LPSs cases considered.
To support preparations for ITER burning plasmas it is important to compare PFPO and FPO plasma parameters that could mutually affect the fast particles and micro-turbulence at the same time and potentially change the thermal and fast particle transport [34,35]. The plasma and fast ion parameters at FPO and PFPO for ITER LPS considered to characterize the interaction with microinstabilities affecting plasma and fast ion transport are discussed in the following. These dimensionless parameters include the external E × B shearing rate [34], γ ExB,ext = |ρ/q dΩ/dρ|, Mach number, M = V tor /C s , rotational shear, dΩ/dρ = (dV tor /dρ)/C s , C s = √ T e /m i is the sound speed, the thermal ion velocity, v i = √ T i /m i . Fast ion 'temperatures' are defined for alphas and suprathermal ions originating from NBI as T f = (2p ⊥,nbi /3 + p ||,nbi /3)/n nbi and T α = p α /n α respectively, where p α , n α are the pressure and density of fast alphas and p ⊥,nbi , p ||,nbi , n nbi are the components of the beam ions perpendicular and parallel to the magnetic field and their density. We also compare the normalized electron pressure, β e = 2µ 0 p e /B 2 , normalized logarithmic gradient of a variable A, R/L A = |RdA/da|, magnetic shear, s = dln (q) /dln (ρ), normalized collisionality [36], ν * = 0.0011 n e RqZ eff (R/a) 3/2 T −2 e . Results of simulations of similar parameters for PFPO and FPO scenarios are summarized in tables 1 and 2. Note that in our simulations sawtooth mixing strongly affects the background plasma transport in the zone X < 0.5, thus, in contrast to [34,35], we consider local values for the parameters above much further from the center, at X = 0.5.
Our comparison reveals that parameters which might affect the impact of fast ions on plasma turbulence are similar for PFPO LPS and the FPO DT scenario plasmas considered (tables 1 and 2). Thus, it looks possible to study the specific impact of fast particles on turbulence features of the low density phase access phase to high Q for the reference DT scenarios during the PFPO-2 phase. Note that detailed local stability analysis requires the dedicated applications of high fidelity codes [34,35], and thus is beyond the scope of our considerations.
From our analyses it is important to emphasize that the dimensionless parameters considered in [34,35] have an impact on the destabilization (R/L pf , R/L T ) and stabilization (γ ExB,ext , β e , ν * , s) of the turbulence. These are predicted to be similar in the LPSs PFPO and FPO scenarios and are close to the values which are predicted to have noticeable impact of the turbulent transport in high fidelity simulations [34,35]. As an example, the predicted normalized fast ion pressure gradient in the low density PFPO and FPO regimes reaches the level R/L pf > 16, which in high fidelity simulations [35] is sufficient for driving of the TAEs and appearance of the zonal flows leading to noticeable reduction of the turbulent transport. This impacts the predictions of plasma parameters of FPO with the 'first principle' models such as [37], which should be extended to incorporate such effects, and the PFPO LPS plasmas offer an opportunity to validate such predictions since the impact on FPO scenarios can be significant. Cases 11-13 are simulated in hydrogen plasma for B t /I p = 1.8/5 T MA −1 with P ECH = 20 MW O-mode third harmonic ECH, and P NBI = 10 MW hydrogen NBI with E NBI = 540 keV. N = 11, 12 correspond to simulations with SBM with different rotation, τ ϕ = 1.24 τ E , τ ϕ = 2 τ E , ∆t FT = 1200 s, N = 13 corresponds to GLF23 with τ ϕ = 2 τ E , ∆t FT = 1340 s.
In addition to possible effects of fast particles on turbulence, we also consider the stability of the fast particles in these PFPO long pulse H-mode plasmas and how this compares to FPO plasmas. For this analysis we applied the non-perturbative Critical Gradient Model (nCGM) [38]. The relaxation of fast ions in the PFPO scenarios is modeled by AE stability calculations using the non-perturbative kinetic ballooning code HINST [39] which computes the local AE growth rates with or without fast ions in general tokamak equilibria. This was shown to give essentially the same results as the perturbative model (pCGM) [40]. In a recent paper by Zou et al [41], the nCGM model was compared with other approaches, demonstrating that the CGM models, in general, could reproduce very accurately the growth and damping rate of AE modes, determine the critical gradient to trigger instabilities as well describing energetic particles finite orbit and Larmor radius effects. Comparison of the low density FPO and PFPO scenarios discussed above shows that the contribution of the ion temperature gradient of thermal ions to AE drive is comparable with the fast ion drive and that the thermal ion drive can strongly affect the AE stability properties. Thermal ions were recently shown to lead to the excitation of AE instabilities with up to n = 200 toroidal mode number in PFPO ITER plasmas [42]. As a result, the impact of AE transport looks similar for the considered FPO and PFPO scenarios. Note that in the central region X < 0.4, the impact of AEs can potentially cause the reduction of the peak fast particle heating and CD efficiency and thus deserves more accurate selfconsistent nonlinear simulations.

Discussion and conclusions
The maximum pulse length achievable in PFPO with no consumption of CS lifetime (ICS ⩽ 30 kA) has been assessed for different heating schemes and confinement regimes in H and He plasmas. Scaling formulae have been derived for the duration of the plasma current flattop in scenarios when the CS discharge starts with initial currents in the coils of about +30 kA and +20 kA based on DINA code free boundary equilibrium modeling as a function of the flattop current, ∆Ψ FT (I p ). This enables the rescaling of results published earlier ( [1,2]) for full CS pre-magnetization.
Simulation of the plasma characteristics for the current flattop was carried out with ASTRA 1.5D self-consistent transport simulations with fixed boundary equilibrium using the separatrix calculated by DINA. The loop voltage, U loop is calculated for each scenario to estimate the duration of the current flattop, ∆t FT = ∆Ψ FT /U loop . Sensitivity to plasma species, heating mix and plasma density have also been studied in our simulations.
With this modeling approach, we show that long-pulse operation is possible in PFPO in L-mode and H-mode plasmas with no significant consumption of CS lifetime. H-mode long pulse operation is viable both with H and He plasmas, although the margin for the earlier is not very large (P SOL /P LH − 1 = 0.2 ÷ 0.25). Operation in H long pulse H-modes in PFPO requires careful control of the shine-through loads for NBI and ECH. This requires ECH in X-mode for half-field operation and tuning of the NBI energy and seeding by Ne to increase neutral ionization. Using these approaches and adjusting the 4 He impurity level, it is possible to heat H plasmas with the 3-ion ICR heating scheme for fields and currents of 3.13 T/8.8 MA.
The current drive efficiency and plasma conductivity in such PFPO LPS H-mode scenarios are high, making possible H-mode plasmas with a flattop length ∆t FT ∼ 1000 s, even with reduced CS currents (+30 kA). This flat top length is comparable with that of LPS in DT operation with a fully charged CS. The results of simulation of the current flattop length for the specific H-mode LPSs modeled in this paper are summarized in figure 12. Note that in our simulations we modeled transport caused by saw-tooth oscillations. This reduces the predicted temperatures in the saw-tooth affected area (X < 0.5) lowering the current driven non-inductively and increasing the plasma resistivity. Therefore, the assessed flat-top duration in our analyses is conservative.
Our simulations reveal many similarities between the plasma properties of PFPO LPSs and the access phases to high Q scenarios in FPO for which the plasma density is in the range n e ∼ 0.4-0.5 n GW . These are, in particular, a high fraction of the fast ion pressure, β fast /β tot ∼ 10-25%, a similar impact of fast ions on plasma turbulence, a wide zone of the weak reversed magnetic shear between sawteeth, a long period between sawteeth (several tens of seconds), a high fraction of driven current and high central rotation (V tor (0) ∼ 400-500 km s −1 for τ ϕ = 2 τ E ). The predicted normalized beta is also similar, β N ∼ 1.5-2, far from the ideal MHD limit, β N < 4 l i , (see figure 11). Note that this is different for the ITER steady state scenario flattop-burn conditions with Q = 5 and n e ∼ 0.7 n GW ; this operates near the stability limit and has no sawteeth (q min > 1) [8]. Operation with infrequent sawteeth oscillations,τ ST ≫ τ E , with WRS in present day experiments can lead to confinement better than the regular H-mode, H y2,98 > 1 [43] if triggering of neoclassical tearing modes is avoided and this mechanism for confinement enhancement together with impact of fast particle effects could also be explored in these PFPO LPSs plasmas. Such enhanced confinement would facilitate access to high Q phases of DT scenarios in FPO through a faster build-up of the alpha heating after the L-H transition and, thus, an earlier validation of such effects could have a significant and positive impact of the FPO Research Plan.

Disclaimer
ITER is the Nuclear Facility INB No. 174. The views and opinions expressed herein do not necessarily reflect those of the ITER Organization.