Plasma Elongation Research Articles

Improved model for transport driven by drift modes in tokamaks

A comparison is made between two versions of the Weiland model for computing anomalous transport driven by drift modes such as the ion temperature gradient (ITG) and trapped electron mode (TEM) in tokamak plasmas. Both are quasilinear fluid models that include physical effects resulting from finite β, magnetic shear, electron-ion collisions, impurities, and fast ions. An outline of the derivation is presented for the newer Weiland19 model, which includes a more accurate description of the effects of finite β, low and negative magnetic shear, plasma elongation, varying correlation lengths, particle pinch, and momentum transport. It is shown that the two models produce nearly the same ion thermal diffusivity as a function of normalized temperature gradient in a circular plasma with moderate magnetic shear, low β, and moderately low density gradient. The models differ significantly at low magnetic shear and in elongated plasmas with high β. In addition, the two models differ significantly in the behavior of the transition between moderate transport driven by ITG/TEM modes at low β and large transport driven by magnetohydrodynamic instabilities at high β. In the older Weiland14 model, the transition occurs at a low value of β that is insensitive to plasma elongation and magnetic shear. In the newer Weiland19 model, the transition occurs at a relatively large value of β that is a sensitive function of plasma elongation and magnetic shear.

A family of analytic equilibrium solutions for the Grad–Shafranov equation

A family of exact solutions to the Grad–Shafranov equation, similar to those described by Atanasiu et al. [C. V. Atanasiu, S. Günter, K. Lackner, and I. G. Miron, Phys. Plasmas 11, 3510 (2004)], is presented. The solution allows for finite plasma aspect ratio, elongation and triangularity, while only requiring the evaluation of a small number of well-known hypergeometric functions. Plasma current, pressure, and pressure gradients are set to zero at the plasma edge. Realistic equilibria for standard and spherical tokamaks are presented.

Efficient plasma and bubble generation underwater by an optimized laser excitation and its application for liquid analyses by laser-induced breakdown spectroscopy

Laser-induced breakdown spectroscopy (LIBS) measurements were performed on bulk water solutions by applying a double-pulse excitation from a Q-Switched (QS) Nd:YAG laser emitting at 1064 nm. In order to optimize the LIBS signal, laser pulse energies were varied through changing of the QS trigger delays with respect to the flash-lamp trigger. We had noted that reduction of the first pulse energy from 92 mJ to 72 mJ drastically improves the signal, although the second pulse energy was also lowered from 214 mJ to 144 mJ. With lower pulse energies, limit of detection (LOD) for Mg in pure water was reduced for one order of magnitude (34 ppb instead of 210 ppb). In order to explain such a phenomenon, we studied the dynamics of the gas bubble generated after the first laser pulse through measurements of the HeNe laser light scattered on the bubble. The influence of laser energy on underwater bubble and plasma formation and corresponding plasma emission intensity were also studied by photographic technique. From the results obtained, we conclude that the optimal first pulse energy should be kept close to the plasma elongation threshold, in our case about 65 mJ, where the gas bubble has its maximum lateral expansion and the secondary plasma is still well-localized. The importance of a multi-pulse sequence on the LIBS signal was also analyzed, where the pulse sequence after the first QS aperture was produced by operating the laser close to the lasing threshold, with the consequent generation of relaxation oscillations. Low-energy multi-pulses might keep the bubble expansion large prior to the probing pulse, but preventing the formation of secondary weak plasmas in multiple sites, which reduces the LIBS signal. The short interval between the pre-pulses and the probing pulse is another reason for the observed LIBS signal enhancement.

Real time control of the plasma current and elongation in tokamaks using ECRH actuators

Real time control of the plasma elongation and plasma current using electron cyclotron resonance heating (ECRH) actuators has been demonstrated on TCV. Tokamak plasmas may be elongated by off-axis ECRH. The associated flattening of the current density profile increases the plasma's vertical stability, enabling higher elongations to be obtained, at lower currents than would be possible in Ohmic conditions. Successful experiments were carried out on TCV to control, in real time, the magnitude of the elongation and the ECRH deposition location using second harmonic ECRH power and ECRH launcher mirror angle actuators. Plasma current control in fully non-inductive plasmas using ECRH actuators to drive ECCD was also demonstrated.

Progress towards steady state at low aspect ratio on the National Spherical Torus Experiment (NSTX)

Modifications to the plasma control capabilities and poloidal field coils of the National Spherical Torus Experiment (NSTX) have enabled a significant enhancement in shaping capability which has led to the transient achievement of a record shape factor (S ≡ q95 (Ip/a Bt)) of ∼41 (MA m−1 T−1) simultaneous with a record plasma elongation of κ ≡ b/a ∼ 3. This result was obtained using isoflux control and real-time equilibrium reconstruction. Achieving high shape factor together with tolerable divertor loading is an important result for future ST burning plasma experiments as exemplified by studies for future ST reactor concepts, as well as neutron producing devices, which rely on achieving high shape factors in order to achieve steady state operation while maintaining MHD stability. Statistical evidence is presented which demonstrates the expected correlation between increased shaping and improved plasma performance. Plasmas with high shape factor have been sustained for pulse lengths which correspond to τpulse = 1.6s ∼ 50 τE ∼ 5 τCR, where τCR is the current relaxation time and τE is the energy confinement time. Plasmas with higher βt ∼ 20% have been sustained for τpulse = 1.2s ∼ 25 τE ∼ 3 τCR with non-inductive current fractions fNI ∼ 50%, with ∼40% pressure driven current and ∼10% neutral beam driven current. An interesting feature of these discharges is the observation that the central value of the safety factor q(0) remains elevated and constant for several current diffusion times without sawteeth, similar to the ‘hybrid mode’. Calculations of the profiles of inductive and non-inductive current are compared with measurements of the total current profile and are shown to be in quantitative agreement. Results are shown from experiments which investigate the applicability of high harmonic fast waves (HHFWs) and electron Bernstein waves (EBWs) as current drive and heating sources, and the possibility of LHCD for future ST devices is raised. A calculated scenario which provides 100% non-inductive current drive is described. NSTX operates with peak divertor heat fluxes which are in the same range as those expected for the ITER device, i.e. with . High triangularity, high elongation plasmas on NSTX have been demonstrated to have reduced peak heat flux to the divertor plates to <3 MW m−2.

The conceptual design for the modification of HL-2A tokamak

HL-2A has achieved parameters of I p = 400 kA, B t = 2.65 T, approaching to its rated operational parameters with I p = 450 kA and B t = 2.8 T so far. Considering present status of HL-2A tokamak and in order to extend experimental research further, the HL-2A will be modified with a more efficient divertor. The objective of modification of HL-2A is to obtain optimized plasma parameters and shape, and an advanced divertor. The plasma configuration will be realized by composite arranging of poloidal field coil (PFC) system. After modification, the plasma current I p will reach 800 kA, the elongation and triangularity of plasma will be above 1.6 and 0.3, respectively.

Plasma shape stabilization of current rise MHD instabilities in TCV

The well-known and potentially disruptive plasma ‘current rise’ instabilities are studied as a function of the plasma shape in the Tokamak à Configuration Variable (TCV). Disruptions typically occur in quasi-circular plasmas at qa ∼ 3 in both non-sawtoothing and sawtoothing discharges with peaked current profiles. The perturbations in the plasma parameters before disruption are characterized, and the main unstable modes identified as coupled m/n = 2/1 and 3/2 rotating tearing modes. In the early phase, coupling between 3/1 and 2/1 modes is found to play a major role in determining whether or not the disruption will occur. Plasma cross section shaping is observed to reduce or to completely stabilize the disruptive mode and is regularly used in TCV operation as a tool for safe initial current ramp-up. Plasma elongation, positive and negative triangularity prevent the growth of a large 2/1 mode at qa ∼ 3, thus reducing or even suppressing the disruptions. We also attempt an interpretation of the experimental results. Calculations of the tearing-mode stability parameter Δ′ using the experimental plasma equilibria suggest the dominant role of toroidal mode coupling in the destabilization of the m/n = 2/1 mode in quasi-circular TCV plasmas. The effect of shaping on the reconstructed current profile and tearing stability is then considered. The analysis shows a destabilising trend with elongation and triangularity in contrast with the experiment. Other stabilizing mechanisms are discussed and shown to potentially contribute to the safe crossing of qa = 3 in shaped plasmas.

Sawtooth behaviour in highly elongated TCV plasmas

The effect of plasma elongation κ on the sawtooth behaviour is studied in ohmically heated TCV plasmas up to values of κ = 2.8. Above a certain value of κ, which varies from 2.2 to 2.6 and depends on the current profile, the sawtooth oscillations disappear completely. The sawteeth are then replaced by continuous oscillations with frequencies in the range from 5 to 20 kHz, which are resonant at the q = 1 surface and seem to prevent a peaking of the temperature and pressure profiles in the plasma core. It is suggested that the transition is a consequence of an ideal internal kink mode becoming unstable, even with a flat pressure profile inside the q = 1 surface, if κ is sufficiently high.

Numerical analyses of high‐beta spherical tokamaks with varied elongation

AbstractThe effect of plasma elongation on the second‐stable spherical tokamak (ST) was numerically studied using the experimentally measured pressure and current profiles of ultrahigh‐beta STs. The maximum beta of ST over 50% was obtained in the TS‐3 ST/CT experiment by applying an external toroidal field to an FRC. It was found that the marginal beta for the ballooning instability increased with the plasma elongation κ of ST. The elongated STs with κ &gt; 2 have the magnetic shear (S)–pressure gradient (α) profiles located in the second‐stable regime for the ballooning mode and the stability margin increased with κ. The close relation between the absolute minimum‐B profile and the second stability was documented. The effect of elongation on maximum beta was observed to saturate when κ exceed 3, indicating that the optimized elongation for high‐beta STs is located around 2 &lt; κ &lt; 3. © 2006 Wiley Periodicals, Inc. Electr Eng Jpn, 155(4): 1–6, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.20132

Spherical tokamak with a plasma center column

Low aspect ratio toroidal pinches such as the standard (q&amp;gt;1) and the ultralow q (q&amp;lt;1) spherical tori or tokamaks (ST), would have a far more robust reactor engineering design if a plasma center column (PCC) can be used in place of a material center post. Biased electrodes across the plasma center column would drive a plasma current to produce the toroidal magnetic field in lieu of the toroidal field (TF) coils. The operation of such a device is naturally divided into two distinct phases: formation by driven relaxation under magnetic helicity injection and sustainment by auxiliary current drive and heating such as rf and neutral beam injection (NBI). The initial design constraints of a ST-PCC experiment are primarily motivated by the formation rather than the sustainment physics. With a Taylor-relaxed plasma as the baseline case, it is shown that three essential factors guide the design. First, the flux amplification factor determines the aspect ratio of the ST-PCC. Second, the plasma shaping in general and plasma elongation in particular gives the most freedom in shaping the q profile of the relaxed plasma. Two examples are the standard spherical tokamak with q&amp;gt;1 throughout the plasma and the ultralow q (ULQ) spherical tokamak with q much less than unity for the bulk of the plasma. Third, the vacuum bias magnetic flux plays the second most important role in modifying the q profile. As an example, it is shown how the bias flux can be designed to delineate a standard spheromak experiment from that of an ULQ ST-PCC. These physics understandings help define the design space of the ST-PCC experiments and directions for optimization.

Structure and scaling properties of the geodesic acoustic mode

Characteristics and scaling properties of the geodesic acoustic mode (GAM), a coherent, radially-sheared high frequency (∼15 kHz) zonal flow oscillation, are studied systematically using time-delay-estimation techniques applied to localized, multi-point density fluctuation measurements obtained by beam emission spectroscopy on DIII-D. The GAM amplitude is shown to increase strongly with increasing safety factor, q95, and to likewise become undetectably small for q95 < 4.2, qualitatively consistent with theoretical predictions based on collisional damping as well as simulations. The radial structure of the GAM exhibits peak amplitude in the radial range 0.88 < r/a < 0.95 with a rapid amplitude reduction inside and outside this region. The measured frequency is close to the predicted frequency, though some deviation to higher frequency is observed at lower q. The GAM amplitude is also shown to increase with plasma elongation, κ, while its frequency decreases.

Progress towards steady state on NSTX

In order to reduce recirculating power fraction to acceptable levels, the spherical torus concept relies on the simultaneous achievement of high toroidal β and high bootstrap fraction in steady state. In the last year, as a result of plasma control system improvements, the achievable plasma elongation on NSTX has been raised from κ ∼ 2.1 to κ ∼ 2.6—approximately a 25% increase. This increase in elongation has led to a substantial increase in the toroidal β for long pulse discharges. The increase in β is associated with an increase in plasma current at nearly fixed poloidal β, which enables higher βt with nearly constant bootstrap fraction. As a result, for the first time in a spherical torus, a discharge with a plasma current of 1 MA has been sustained for 1 s (0.8 s current flat-top). Data are presented from NSTX correlating the increase in performance with increased plasma shaping capability. In addition to improved shaping, H-modes induced during the current ramp phase of the plasma discharge have been used to reduce flux consumption and to delay the onset of MHD instabilities. Based on these results, a modelled integrated scenario, which has 100% non-inductive current drive with very high toroidal β, will also be discussed. The NSTX poloidal field coils are currently being modified to produce the plasma shape which is required for this scenario, which requires high triangularity (δ ∼ 0.8) at elevated elongation (κ ∼ 2.5). The other main requirement of steady state on NSTX is the ability to drive a fraction of the total plasma current with RF waves. The results of high harmonic fast wave heating and current drive studies as well as electron Bernstein wave emission studies will be presented.

The ARIES-AT advanced tokamak, Advanced technology fusion power plant

The ARIES-AT study was initiated to assess the potential of high-performance tokamak plasmas together with advanced technology in a fusion power plant and to identifying physics and technology areas with the highest leverage for achieving attractive and competitive fusion power in order to guide fusion R&D. The 1000-MWe ARIES-AT design has a major radius of 5.2 m, a minor radius of 1.3 m, a toroidal β of 9.2% ( β N = 5.4) and an on-axis field of 5.6 T. The plasma current is 13 MA and the current-drive power is 35 MW. The ARIES-AT design uses the same physics basis as ARIES-RS, a reversed-shear plasma. A distinct difference between ARIES-RS and ARIES-AT plasmas is the higher plasma elongation of ARIES-AT ( κ x = 2.2) which is the result of a “thinner” blanket leading to a large increase in plasma β to 9.2% (compared to 5% for ARIES-RS) with only a slightly higher β N. ARIES-AT blanket is a simple, low-pressure design consisting of SiC composite boxes with a SiC insert for flow distribution that does not carry any structural load. The breeding coolant (Pb–17Li) enters the fusion core from the bottom, and cools the first wall while traveling in the poloidal direction to the top of the blanket module. The coolant then returns through the blanket channel at a low speed and is superheated to ∼1100 °C. As most of the fusion power is deposited directly into the breeding coolant, this method leads to a high coolant outlet temperature while keeping the temperature of the SiC structure as well as interface between SiC structure and Pb–17Li to about 1000 °C. This blanket is well matched to an advanced Brayton power cycle, leading to an overall thermal efficiency of ∼59%. The very low afterheat in SiC composites results in exceptional safety and waste disposal characteristics. All of the fusion core components qualify for shallow land burial under U.S. regulations (furthermore, ∼90% of components qualify as Class-A waste, the lowest level). The ARIES-AT study shows that the combination of advanced tokamak modes and advanced technology leads to an attractive fusion power plant with excellent safety and environmental characteristics and with a cost of electricity (4.7 ¢/kWh), which is competitive with those projected for other sources of energy.

Direct measurement of neoclassical currents using motional Stark effect polarimetry

The radial profile of the Pfirsch–Schlüter current has been measured directly for the first time in a tokamak using motional Stark effect (MSE) polarimetry. The MSE diagnostic measures the vertical component of the magnetic field (Bz) as a function of the plasma major radius. The analysis technique presented here converts the experimental Bz profile into a flux-surface-average current density as well as a local current density. Taking the appropriate difference between these two quantities yields a direct measurement of the Pfirsch–Schlüter current density, and consequently a MSE-based measurement of the plasma pressure profile. The bootstrap current density can also be directly determined from the Bz profile (with greater approximation) in the collisionless limit. An equilibrium reconstruction is not required for this MSE analysis technique, although a few basic geometric parameters such as the plasma minor radius, elongation and triangularity need to be known. The usefulness of this approach for analysing the current profile is demonstrated using discharges from the DIII-D tokamak.

Slow Formation of Spherical Tokamak by ECH on LATE

The main objective of LATE is to demonstrate the formation of Spherical Tokamak (ST) by electron cyclotron heating (ECH) alone without the center solenoid. In the last year, as a result of the extended microwave power from 10 to 30kW and introducing the vertical plasma position control system, the achievable plasma current has been raised substantially compared with the results reported previously(1). With a two-seconds pulse of 2.45GHz microwave power up to 30kW, a plasma current of 2.0kA have been spontaneously initiated under the steady vertical field, then ramped-up slowly to 7.2kA with a slow ramp-up of the vertical field strength (Bv) for the equilibrium of the plasma current loop. The Bv decay index is temporally-controlled during the discharge to successfully increase the plasma elongation with the aid of the active control of the vertical plasma position. This increase in elongation has lead to an effective increase in the plasma current. Magnetic analysis shows that an ST equilibrium, having the last closed flux surface with an aspect ratio of R0 / a = 20.5cm/14.8cm 1.4, an elongation of κ 1.6 and qedge 34, has been finally formed and maintained steady until the end of the microwave pulse.

Numerical Analysis of High-beta Spherical Tokamaks with Varied Elongation

The effect of plasma elongation on the second-stable spherical tokamak (ST)was numerically studied using the experimentally measuredpressure and current profiles of ultra-high beta STs. The maximum beta of ST over 50% was obtained in the TS-3 ST/CT experimentby applying an external toroidal field to an FRC. It was found that the marginal beta for the ballooning instabilityincreased with the plasma elongation κ of ST. The elongated STs with κ > 2 have the magnetic shear (S) -- pressure gradient(α) profiles located in the second-stable regime for the ballooning mode andthe stability margin increased with κ. The close relation between the absolute minimum-B profile andthe second stability was documented. The effect of elongation on maximum beta was observed to saturatewhen κ exceeded 3, indicating that the optimized elongationfor high-beta STs are located around 2 < κ < 3.

Numerical studies of a steady state axisymmetric co-axial helicity injection plasma

Steady state current profile, plasma potential, and plasma flow of an electrostatically driven co-axial helicity injection (CHI) plasma with axisymmetry are numerically investigated using both an open field line Grad–Shafranov equilibrium model and self-consistent initial value magnetohydrodynamic (MHD) simulations. For CHI plasmas, the Grad–Shafranov model ignores plasma inertia but not a perpendicular, or Grad–Shafranov, flow. The Grad–Shafranov flow is the result of the gradient of Grad–Shafranov potential across magnetic field lines, and is responsible for toroidal current drive. Numerical Grad–Shafranov solutions show that as the characteristic CHI discharge parameter, the normalized voltage V̂≡μ0V/ηB0q0, becomes order of unity, CHI plasma develops kink-unstable hollow current profile. Here 𝒱 is the imposed voltage, η the plasma resistivity, q0 the toroidal and injector poloidal flux ratio, and B0≡4χ0/ab a nominal poloidal field defined by the injector poloidal flux χ0, plasma minor radius a, and plasma elongation b/a. When a small plasma inertia is included in the equation of motion, such as that in a time dependent MHD calculation, the modification on the perpendicular current is small, but its impact on parallel current distribution and hence the spatial dependence of magnetic flux can be great through the Pfirsch–Schlüter-like effects.

The basics of spherical tokamaks and progress in European research

When the aspect ratio of a tokamak (A = R/a) decreases significantly, there is a transformation of the well studied tokamak toroidal magnetic configuration into the spherical tokamak (ST) configuration. This configuration has high natural plasma elongation and triangularity and other unique equilibrium and stability properties of ST configuration, which are discussed in this paper.European research into ST physics is well advanced in spite of the young age of this branch of fusion science. An overview of selected experimental and theoretical results obtained at Ioffe, Culham and Frascati is given with the emphasis on their complementarity and links to the main stream of tokamak research, such as ITER. An outline of the basic ST advantages and the potential of ST research for new insights into magnetic confinement is also given. More detailed descriptions of recent advances in ST theory and experiment may be found in the invited papers by Akers and Ono in the proceedings of this conference.

Effects of plasma shape on laser blow-off injected impurity transport in TCV

The extreme shaping capabilities of the TCV tokamak have been used to investigate the effect of plasma geometry on the confinement of non-recycling trace impurities injected by means of the laser blow-off technique. The progression of the injected silicon in the core of TCV Ohmic limiter plasmas was followed by the 200-channel soft x-ray (SXR) photodiode array with good spatial and temporal resolution. The results show that the plasma triangularity and elongation play an important role in the impurity confinement time, τimp. Remarkably, the increase of elongation from κ = 1.6 to 2.3 produces a threefold reduction of τimp while the electron energy confinement time, τEe, remains almost constant. τimp is fairly constant in the triangularity scan for δ > 0.2, while there is a marked increase for lower values, leading to τimp > 100 ms for negative triangularities. The increase of the toroidal magnetic field, BT, from BT = 0.92 to 1.47 T produces a decrease in the confinement time by almost a factor of 2. Simulation of the evolution of the line-integrated SXR signals, performed by the one-dimensional code STRAHL, provided both central and peripheral values of the transport coefficients together with estimates of the radial profiles. The simulations show that anomalous transport is dominant over neoclassical transport, except near the plasma centre. Interestingly, the convective velocity is positive (outwardly directed) in all limiter cases.

Precession of toroidally passing particles in tokamaks and spherical tori

The toroidal precession of the circulating particles and semitrapped particles (toroidally passing but poloidally trapped particles) is studied. Expressions for the precession frequency, which are convenient for practical use, are obtained and analyzed. It is found that the key parameters that determine the magnitude and the direction of the precession velocity are the plasma elongation, the magnitudes and profiles of the safety factor and β defined as the ratio of the local plasma pressure to the magnetic field pressure at the magnetic axis. An important role of the “paramagnetic” precession in highly elongated plasmas is revealed. The analysis carried out is based on the obtained expressions for the equilibrium magnetic field strength and the field line curvature.