Trapped Alpha Particles Research Articles

Collisional alpha transport in a weakly non-quasisymmetric stellarator magnetic field

Alpha particle confinement is a serious concern in stellarators and provides strong motivation for optimizing magnetic field configurations. In addition to the collisionless confinement of trapped alphas in stellarators, excessive collisional transport of the trapped alpha particles must be avoided while they tangentially drift due to the magnetic gradient (the $\unicode[STIX]{x1D735}B$ drift). The combination of pitch angle scatter off the background ions and the $\unicode[STIX]{x1D735}B$ drift gives rise to two narrow boundary layers in the trapped region. The first is at the trapped–passing boundary and enables the finite trapped response to be matched to the vanishing passing response of the alphas. The second layer is a region that encompasses the somewhat more deeply trapped alphas with vanishing tangential $\unicode[STIX]{x1D735}B$ drift. Away from (and between) these boundary layers, collisions are ineffective and the alpha $\unicode[STIX]{x1D735}B$ drift simply balances the small radial drift of the trapped alphas. As this balance does not vanish as the trapped–passing boundary is approached, the first collisional boundary layer is necessary and gives rise to $\surd \unicode[STIX]{x1D708}$ transport, with $\unicode[STIX]{x1D708}$ the collision frequency. The vanishing of the tangential drift results in a separate, somewhat wider boundary layer, and significantly stronger superbanana plateau transport that is independent of collisionality. The constraint imposed by the need to avoid significant energy depletion loss in the slowing down tail distribution function sets the allowed departure of a stellarator from an optimal quasisymmetric configuration.

Lower hybrid wave produced supra-thermal electrons and fishbone-like instability in FTU

The fishbone-like internal kink instability driven by supra-thermal electrons generated by lower hybrid current drive is an important issue of burning plasma research. Indeed, the trapped particle averaged bounce characterizing the interaction of trapped alpha particles with low-frequency MHD modes in burning plasmas depends on energy, not on mass, hence the charged fusion product effects can be usefully modelled by the analogous effect induced by the fast electrons on the low-frequency MHD modes.Fishbone-like internal kink instabilities driven by electrons were observed during experiments on Frascati Tokamak Upgrade (FTU) and interpreted in terms of an oscillating ‘fixed point’ activity followed by one of ‘limit cycle’, produced by suprathermal electrons in the presence of a q-profile with qmin ≈ 1. As an interesting behaviour of the fast electron population produced by the LH power when the q-profile meets the condition qmin ≈ 1, the fast electron bremsstrahlung data of FTU show a marked redistribution in space across layers centred at r/a ≈ 0.20–0.33. This redistribution occurs during and in phase with the fishbone oscillation observed by the MHD diagnostic, with the same time scale and at the same radial position of the peak emission seen by x-ray tomography.

Electron fishbones: theory and experimental evidence

We discuss the processes underlying the excitation of fishbone-like internal kink instabilities driven by supra-thermal electrons generated experimentally by different means: electron cyclotron resonance heating (ECRH) and by lower hybrid (LH) power injection. The peculiarity and interest of exciting these electron fishbones by ECRH only or by LH only is also analysed. Not only is the mode stability explained, but also the transition between steady state nonlinear oscillations to bursting (almost regular) pulsations, as observed in FTU, is interpreted in terms of the LH power input. These results are directly relevant to the investigation of trapped alpha particle interactions with low-frequency MHD modes in burning plasmas: in fact, alpha particles in reactor relevant conditions are characterized by small dimensionless orbits, similarly to electrons; the trapped particle bounce averaged dynamics, meanwhile, depends on energy and not mass.

Alfvénic instabilities driven by fusion generated alpha particles in ITER scenarios

The stability of proposed ITER scenarios with respect to low-medium mode number Alfvénic instabilities driven by fusion-produced alpha particles is investigated by hybrid MHD-particle simulations. Three cases are considered: the monotonic safety factor scenario (SC2), the reversed-shear one (SC4) and a flat safety factor profile ‘hybrid’ scenario (SCH). All the three cases are found unstable, even though the mode growth rates are quite small. The investigation is extended to cases with larger drive, which could be realistically obtained because of a moderate increase in electron and bulk-ion temperatures as well as by inclusion of energetic particles produced by additional heating methods. It is shown that, in the SCH case, if the drive exceeds the reference value by a factor ∼1.6, fast growing energetic-particle modes (EPMs) are driven unstable by the resonance with trapped alpha particles. The effects of nonlinear mode dynamics on the alpha-particle confinement at the reference drive are negligible for the SC2 and the SCH cases. For the SC4 scenario, some broadening of the alpha-particle pressure profile is observed, indicating inconsistency problems of the scenario itself. Simulations performed with increasing drive intensity show that a strong flattening of the alpha-particle pressure profile can occur in the inner plasma region for the SC2 case, while global confinement is not significantly affected. In the SC4 and SCH scenarios nonlinear effects are more pronounced in the outer portion of the discharge, where the modes are localized, with less impact on the on-axis pressure value with respect to the SC2 case. While for SCH such effects are observed only above the threshold for EPM destabilization, in the SC4 case significant alpha particle losses can occur even at moderately increased drive.

Simulation study of relativistic dynamics of MeV alpha particles in magnetized plasmas for explaining an experimental anomaly

In a Test Fusion Tokamak Reactor [R. J. Hawryluk et al., Phys. Plasmas 5, 1577 (1998)] experiment, the measured energy spectrum of the deeply trapped alpha particles is found to be 1MeV too broad to be explained by classical collisions and the peak energy similarly off by 450keV. The relativistic effect is proposed as an explanation. Here, we report high-resolution Monte Carlo (MC) and particle-in-cell (PIC) simulation studies in detail, under the assumption of a uniform magnetic field, for the identification of the cause of the observed anomaly. The 3.5MeV alpha particles produced by thermonuclear fusion reaction are broadened due to Doppler effect. The relativistic alpha particle dynamics are followed with the PIC code. The relativistic ion cyclotron instability grows to saturation on a time scale (10−5s) much shorter than the experimental time scale of 0.1s. The MC code is then used to follow, in real time, the collisional slowing down of the gyrobroadened alphas, including the effect of the time delay in diagnostic pellet releasing and flight. Relativistic gyrobroadening is shown to be crucial in shaping the birth and slowed-down spectra. The resultant alpha particle energy spectrum fits well with that of the measurement, with a reduced chi square of unity.

Bounce precession fishbones in the national spherical torus experiment

Bursting modes, which are identified as bounce precession frequency fishbone modes, are observed on a low aspect ratio tokamak, the national spherical torus experiment (Ono M. et al 2000 Nucl. Fusion 40 557). They are predicted to be important in high current, low shear discharges with a significant population of trapped particles with a large mean bounce angle, such as produced by near tangential beam injection into a small aspect ratio device. Such a distribution is often stable to the usual precession-resonance fishbone mode. These modes could be important in ignited plasmas, driven by the trapped alpha particle population.

Alpha-tail production with ion-cyclotron-resonance heating of 4He-beam ions in JET plasmas.

Third-harmonic ion-cyclotron-resonance heating of 4He-beam ions has produced for the first time on the JET tokamak high-energy populations of 4He ions to simulate 3.5 MeV fusion-born alpha (alpha) particles. Acceleration of 4He ions to the MeV energy range is confirmed by gamma-ray emission from the nuclear reaction 9Be(alpha,ngamma) 12C and excitation of Alfvén eigenmodes. Concomitant electron heating and sawtooth stabilization are observed. The scheme could be used in next-step tokamaks to gain information on trapped alpha particles and to test alpha diagnostics in the early nonactivated phase of operation.

Injection of He2+ Ions at a parallel shock

Abstract The very initial acceleration from thermal to supra-thermal energies at collisionless shocks is still under debate. The present work is an extension of the injection and acceleration model at quasi-parallel shocks (Sugiyama and Fujimoto, 1999), in which large-amplitude monochromatic upstream waves play the key role. Some upstream protons are selected out of the thermal population during their first encounter with the shock and are accelerated to several times the ram energy (E 0 ) when they are injected into the upstream / downstream region. The injection and acceleration take place very quickly within a few times the inverse upstream proton gyro-frequency Ω i −1 . Here, we have applied this injection model to alpha particle (He 2+ ) and demonstrated that the same process works. Both in test particle calculation and hybrid simulation, it is observed that selected alpha particles are accelerated to a suprathermal energy level. In a test particle calculation, some of the selected alpha particles stay around the shock much longer (20 Ω i −1 ) and are accelerated to considerably higher energy (50 E 0 ) than protons (∼10 E 0 ). In a hybrid simulation, however, such long trapped alpha particles are not detected. This difference suggests that in a realistic self-consistent shock system, there is an/are additional process(es) to release the alpha particles from a shock region before sufficient acceleration occurs. Otherwise, the shock structure would be strongly modified by the presence of a significant energy flow into the highly energized alpha particles.

Energetic particle physics in JET

Results achieved on JET during the 1997-1999 experimental campaigns in the physics of energetic ions and runaway electrons are reviewed. Heating of deuterium-tritium (DT) plasmas by fusion born alpha particles is found to be similar to that achieved by comparable ICRF heating of deuterium plasmas. The stability of alpha particle driven Alfvén eigenmodes (AEs) in the highest fusion power ELM-free H mode discharges is shown to be consistent with the existing theoretical analysis for AEs. Direct measurements of the trapped alpha particle and knock-on deuteron distribution functions by a neutral particle analyser (NPA) are described. New ICRF heating scenarios tested in JET DT plasmas are presented in view of the possible use of the ICRF heating of ITER-like DT plasmas on route to ignition. The energetic ion pinch in the presence of toroidally asymmetric ICRF waves is studied experimentally on JET. Recent experimentally observed effects of ICRF accelerated ions on sawteeth in JET are reviewed. Detailed time and space resolved X ray images of the electron runaway beam in flight spontaneously generated by disruptions on JET are described.

Pellet charge exchange measurements of confined alphas in deuterium–tritium plasmas (invited) (abstract)

Alpha particle confinement is essential to achieving ignition in deuterium–tritium plasmas, and measuring the energy and spatial distributions of fusion alphas is one of the most challenging tasks in plasma diagnostics research. Confined trapped-alpha energy spectra and radial density profiles in the Tokamak Fusion Test Reactor (TFTR) have been obtained using the pellet charge exchange (PCX) diagnostic, which measures high energy (Eα=0.5–3.5 MeV), trapped alphas (|v∥/v|=0.048) at a single time slice (Δt∼1 ms) with a spatial resolution of Δr∼5 cm. PCX measures the energy spectrum of energetic helium neutrals resulting from charge exchange interactions of alphas incident on the ablation cloud surrounding small boron and lithium pellets injected radially into TFTR. The success of PCX has led to a number of important results on the behavior of alphas in TFTR. The measured alpha energy spectrum in the plasma core of sawtooth-free discharges is consistent with the alphas being well confined and slowing down classically. Outside the plasma core, the trapped alphas show the effects of stochastic diffusion due to the toroidal magnetic field ripple, with the PCX measured profiles consistent with the functional dependence of the stochastic ripple diffusion on the alpha energy and the q profile. Large sawtooth instabilities result in radial redistribution of the trapped alphas to well outside the q=1 radius and beyond the stochastic ripple loss boundary. Broadening of the radial profiles of trapped alphas is also observed in reversed and reduced shear discharges on TFTR, with potential implications for reactor designs based on optimized shear configurations. Finally, radial redistribution of trapped alpha particles in the presence of core localized Toroidal Alfv́en Eigenmode activity is also observed. Application of PCX measurements to future experiments, including the International Thermonuclear Experimental Reactor will also be discussed.

Confined trapped alpha behaviour in TFTR deuterium-tritium plasmas

Confined trapped alpha energy spectra and differentialradial density profiles in TFTR D-T plasmas were obtained with thepellet charge exchange (PCX) diagnostic, which measures high energy(Eα = 0.5-3.5 MeV) trapped alphas (v||/v = -0.048) at a single time slice (Δt ≈ 1 ms) with a spatialresolution of Δr ≈ 5 cm. Tritons produced in D-Dplasmas and RF driven ion tails (H, 3He or T) were also observedand energetic tritium ion tail measurements are discussed. PCX alphaand triton energy spectra extending up to their birth energies weremeasured in the core of MHD quiescent discharges where the expectedclassical slowing down and pitch angle scattering effects are notcomplicated by stochastic ripple diffusion and sawtooth activity.Both the shape of the measured alpha and triton energy distributionsand their density ratios are in good agreement with TRANSPpredictions, indicating that the PCX measurements are consistent withclassical thermalization of the fusion generated alphas and tritons.From calculations, these results set an upper limit on possibleanomalous radial diffusion for trapped alphas of Dα ⩽ 0.01 m2·s-1. Outside the core, where the trappedalphas are influenced by stochastic ripple diffusion effects, the PCXmeasurements are consistent with the functional dependence of theGoldston-White-Boozer stochastic ripple threshold on the alphaenergy and the q profile. In the presence of strong sawtoothactivity, the PCX diagnostic observes significant redistribution ofthe alpha signal radial profile wherein alphas are depleted in thecore and redistributed to well outside the q = 1 radius, butapparently not beyond the energy dependent stochastic ripple lossboundary. The helical electric field produced during the sawtoothcrash plays an essential role in modelling the sawtoothredistribution data. In sawtooth free discharge scenarios withreversed shear operation, the PCX diagnostic also observes radialprofiles of the alpha signal that are significantly broader thanthose for supershots. ORBIT modelling of reversed shear andmonotonic shear discharges is in agreement with the q dependentalpha profiles observed. Redistribution of trapped alpha particles inthe presence of core localized toroidal Alfvén eigenmode (TAE)activity was observed and modelling of the PCX measurements based ona synergism involving the α-TAE resonance and the effect ofstochastic ripple diffusion is in progress.

Modelling of alpha particle slowing down, confinement and redistribution by sawteeth in TFTR using the FPPT code

Results from recent deuterium-tritium (DT) experiments on TFTR to measure the energy spectra and radial profiles of well trapped confined alpha particle distributions using the pellet charge exchange (PCX) diagnostic in quiescent plasmas are compared with a numerical modelling using the Fokker-Planck post-TRANSP (FPPT) processor code and show a classical slowing down behaviour of the alphas (Fisher, R.K., et al., Phys. Rev. Lett. 75 (1995) 846). However, in the presence of sawtooth oscillations PCX experimental data indicate a significant broadening of the trapped alpha radial distributions (Petrov, M.P., et al., Nucl. Fusion 35 (1995) 1437). Conventional models consistent with measured sawtooth effects on passing particles do not provide satisfactory simulations of the trapped particle mixing measured by the PCX diagnostic. A mechanism is proposed for fast particle mixing during the sawtooth crash to explain the trapped alpha particle radial profile broadening after the crash. The model is based on the fast particle orbit averaged toroidal drift in a perturbed helical electric field with an adjustable absolute value (similar to that in Kolesnichenko, Ya.I., et al., Nucl. Fusion 36 (1996) 159). Such a drift of the fast particles results in a change of their energy and a redistribution id phase space. To show the sensitivity of trapped particles to sawteeth, the redistribution in toroidal momentum Pphi (or in minor radius) was calculated in two ways. The first is based on the assumption that Pphi redistribution is stochastic with a large diffusion coefficient and was taken to be flat. The second way is to apply Kolesnichenko's inversion formula (Kolesnichenko, Ya.I., et al., Nucl. Fusion 32 (1992) 449). Both methods are compared with PCX data. The distribution function in a pre-sawtooth plasma and its evolution in a post-sawtooth crash plasma are simulated using the FPPT code. It is shown that FPPT calculated alpha particle distributions are consistent with TRANSP Monte Carlo calculations. Compariso

Measurements of confined alphas and tritons in the MHD quiescent core of TFTR plasmas using the pellet charge exchange diagnostic

The energy distributions and radial density profiles of the fast confined trapped alpha particles in DT experiments on TFTR are being measured in the energy range 0.5 - 3.5 MeV using the pellet charge exchange (PCX) diagnostic. A brief description of the measurement technique which involves active neutral particle analysis using the ablation cloud surrounding an injected impurity pellet as the neutralizer is presented. This paper focuses on alpha and triton measurements in the core of MHD quiescent TFTR discharges where the expected classical slowing-down and pitch angle scattering effects are not complicated by stochastic ripple diffusion and sawtooth activity. In particular, the first measurement of the alpha slowing-down distribution up to the birth energy, obtained using boron pellet injection, is presented. The measurements are compared with predictions using either the TRANSP Monte Carlo code and/or a Fokker - Planck Post-TRANSP processor code, which assumes that the alphas and tritons are well confined and slow down classically. Both the shape of the measured alpha and triton energy distributions and their density ratios are in good agreement with the code calculations. We can conclude that the PCX measurements are consistent with classical thermalization of the fusion-generated alphas and tritons.

Edge-Localized Thermonuclear Magnetoacoustic-Cyclotron Instability in Tokamaks

The distribution function of fast alpha particles in a tokamak plasma near the outer circumference of the torus is obtained. Calculations are carried out for an axisymmetric tokamak for which the alpha-particle banana width is small in comparison with the plasma radius but sufficiently large to provide the presence of trapped alpha particles, produced in the plasma core, in the plasma edge region. It is shown that alpha particles with this distribution function can excite an edge-localized instability of plasma on magnetoacoustic waves with a frequency close to the harmonics of the alpha-particle gyrofrequency. This contributes to an explanation of the superthermal ion-cyclotron emission observed experimentally on the Joint European Torus (JET) and the Tokamak Fusion Test Reactor (TFTR).

Stabilizing Effect of Trapped Alpha Particles on Low-Frequency MHD Ballooning Modes in ITER Plasmas with Flatq(ψ) Profiles

In this paper the stabilizing compressibility effect of trapped alpha particles on low-frequency magnetohyrodynamic (MHD) ballooning modes (Re[omega] [much lt] Im [omega]) in the International Thermonuclear Experimental Reactor (ITER) is investigated. It is found that this stabilization is the most effective one in the central region of the plasma column, where the unstable region of MHD balloning modes is located for typical flat q([phi]) profiles in ITER. The alpha-particle distribution function is supposed to be isotropic and slowing down in energy. It has been found that the values of [beta][sub [alpha]]/[beta][sub total] (congruet) 1.5 to 2.0% are sufficient to stabilize ballooning modes in the central low-shear region for the peaked pressure profiles [P([phi]) = P(0)(1 [minus] [phi])[sup [gamma]]] proposed for ITER. The value of [beta][sub [alpha]]/[beta][sub total] remains almost unchanged to suppress the instability for all [gamma] = 1.0 to 2.0.

Effects of trapped alpha particles on internal kink modes in tokamaks

The theory of linear interaction between internal kink modes and fusionproduced high-energy alpha particles in a toroidal plasma is extended by including finite-banana-width corrections to the alpha dynamics. An important implication of the theory for the stability properties of kink modes is that the finite-banana-width effects increase the value of the poloidal alpha beta required to attain the stable domain of operation as well as that required to excite the high-frequency fishbone instability. Furthermore, these effects lead to a reduction in the instability growth rate in both the low- and high-frequency unstable regimes.

Alpha-Particle Effects on Ballooning Flute Modes in Tokamaks

In this paper a more accurate dispersion equation for ideal ballooning flute modes in a plasma with alpha particles is obtained. It is shown that circulating and trapped alpha particles generate the eigenbranches of the mode oscillations with frequencies {omega} {approx lt} {omega}{sub *i}, where {omega}{sub *i}, is the ion drift frequency. The relevant growth rates and frequencies are found. It is ascertained that in the frequency range {omega}{sub *i} {lt} {omega} {lt} {bar {omega}{sub Db}}, where {bar {omega}{sub Db}} is the magnetic drift frequency average over a bounce period, trapped alpha particles may generate forced oscillations that influence the ideal ballooning flute mode stability boundary. It is shown that the stability may be improved for certain plasma parameters and trapped alpha-particle pressures.

Alpha-Particle Effects on LOW-n Magnetohydrodynamic Modes

This paper reports that the NOVA-K code is employed to study the effects of alpha particles on two types of magnetohydrodynamic (MHD) modes: the stabilization of ideal MHD internal modes and the excitation of resonant internal modes, and the alpha-particle destabilization of toroidicity-induced Alfven eigenmodes (TAEs) via transit resonances. Analytical theories are also presented to help explain the NOVA-D results. The trapped alpha particles are found to destabilize the n = 1 internal mode and lower the total beta threshold. The circulating alpha particles can strongly destabilize TAE modes via inverse Landau damping associated with the spatial gradient of the alpha-particle pressure.

Energetic particle effects on global magnetohydrodynamic modes

The effects of energetic particles on magnetohydrodynamic (MHD) type modes are studied using analytical theories and the nonvariational kinetic-MHD stability code (nova-k) [Workshop on Theory of Fusion Plasmas, (Societa Italiana di Fisica, Bologna, 1987), p. 185]. In particular, the problems of (1) the stabilization of ideal MHD internal kink modes and the excitation of resonant ‘‘fishbone’’ internal modes and (2) the alpha particle destabilization of toroidicity-induced Alfvén eigenmodes (TAE) via transit resonances are addressed. Analytical theories are presented to help explain the nova-k results. For energetic trapped particles generated by neutral beam injection or ion cyclotron resonant heating, a stability window for the n=1 internal kink mode in the hot particle beta space exists even in the absence of core ion finite Larmor radius effect. On the other hand, the trapped alpha particles are found to resonantly excite instability of the n=1 internal mode and can lower the critical beta threshold. The circulating alpha particles can strongly destabilize TAE modes via inverse Landau damping associated with the spatial gradient of the alpha-particle pressure.

On the stochastic interaction of toroidally trapped alpha particles with lower hybrid waves in the tokamak reactor regime

Lower hybrid waves used for the generation of the driven current can strongly interact with thermonuclear alpha particles on their cyclotron harmonics. For the chosen banana-trapped alpha particles, we calculate their radial diffusion, appearing in the intrinsic stochasticity regime of this interaction; this diffusion seems to be important.