Values Of Βp Research Articles

Electron ITB formation in EAST high poloidal beta plasmas under dominant electron heating

Plasma confinement and transport in tokamaks play a crucial role in the development of high poloidal beta steady-state operation scenarios. Therefore, it is very important to study the relevant mechanism of internal transport barriers (ITBs), which can help plasmas to obtain better confinement in order to achieve higher fusion gain. This paper mainly introduces the analysis of the characteristics of electron heat transport of discharges with ITB in high βP operation regime in Experimental Advanced Superconducting Tokamak (EAST). Based on the statistical analysis of stable discharges with βP > 1.5, it is found that there is an obvious bifurcation of the normalised electron temperature gradient (ETG) ( R/LTe ) in the range of βP = 2–2.2. Then the discharges of lower βP ( βP < 2, where the value of βP is below the bifurcation threshold) and of higher βP ( βP > 2.2, where the value of βP is above the threshold) were selected for analysis. The diagnostic data provided by Thomson scattering, x-ray crystal spectrometry and charge exchange recombination spectroscopy are used to provide reliable parameter profiles and then combined with the data of external magnetic probe measurements and the polarisation interferometer diagnosis system to fully reconstruct the balance. A relevant plasma current calculation model is used to calculate and analyse the current density profiles and power deposition, and then the transport analysis is carried out. Interestingly, in the higher βP discharges, it is found that the turbulence intensity provided by the CO2 laser collective scattering system gradually decreases and the normalised ETG R/LTe gradually increases. It is also found that the electron heat transport coefficient decreases in the discharge with higher βP and the growth rate of the electron-scale turbulence calculated by transport gyro-Landau fluid (TGLF) is significantly reduced. Meanwhile, similar conclusions are also obtained in the discharges when the βP is further increased.

Optimization of Magnetic Confinement for Quasi-Snowflake Divertor Configuration

To realize the commercialized operation, it is preferable that tokamak devices achieve the operating scenarios with steady-state, long-pulse, H-mode and high magnetic confinement plasma current. For enhancing the magnetic confinement capability and improving the poloidal beta βp in quasi-snowflake configuration, under the consideration of the effect on other performance parameters, the method of shifting magnetic axis is employed. According to the calculated method proposed in this paper, the plasma current density distribution is modified to realize the supposed radial movement of the magnetic axis. Then the value of βp, the coordinates of X2 point, the flux expansion of outside and inside strike points (fmout and fmin), poloidal field currents and safety factor q profile are formulated, the relations between these parameters and the horizontal displacement of the magnetic axis are analyzed. Finally, in lower single-null quasi-snowflake configuration, by shifting the magnetic axis from 1.9242 to 1.9412m, βp has an increase of 86.96 %, the confinement capability of the plasma is significantly enhanced, Meanwhile, the position of X2 point is varied from (2.6789 m, −1.6439 m) to (2.2955 m, −1.6039 m), which is closer to X1 point and the plasma. Therefore, fmout is enlarged from 6.646 to 7.706, which has an increase of 15.9%. And fmin has a decrease of 0.62%, which can be neglected. The safety factor at magnetic axis q0 is decreased by 1.75%, from 1.0897 to 1.0701, which is larger than 1 and satisfies the requirement of magnetohydrodynamic stability. In addition, EFIT code is used to verify the feasibility and the accuracy of the optimized results.

Parametric study of iodine-129 releases from nuclear fuel to fuel-clad gap & primary coolant in PWRs

A numerical methodology is developed to compute volatile fission fragment release from fuel to gap and then to the primary coolant under changing reactor conditions. Based on diffusion of fission fragments and mass balances in gap and in coolant, a FORTRAN-77 based program DIFFP (Diffusion of Fission Products) has been developed to solve numerically the time & space dependent equations using source release rate respectively. For power shutdown effect of spiking have been modeled for given release rate. The predicted gas fractional release as a function of time using DIFFP program was in good agreement with the reported results. Then parametric studies for empirical diffusion constant (D′), coolant purification rate (βP), and gas escape rate coefficient (ν) respectively were done to find the sensitivity of parameters. For operation time >150 days, the sensitivity increases from 4.5% to 20.4% with an increase D′ from 4.1 × 10−10 s−1 to 6.9 × 10−10 s−1 respectively and sensitivity is a nonlinear function of D′: sensitivity=(-62.20±0.78)+(16.83±0.37)D′Do′+(-0.703±0.0398)D′Do′2where, 0.69<D′/D0′<1.17 and D′ is the reference value (5.9 × 10−10 s−1) for the defective fuel rods. Sensitivity for gas escape rate coefficient (ν) was also determined by increasing it from 5% to 50% from its reference value (1.4 × 10−4 s−1) and results show that the coolants activity becomes insensitive to changes in the gas escape rate coefficient and sensitivity value becomes less than 1% when effective full power days are larger than 150. If coolant purification rate constant (βP) is parametrically changed from 5% to 30%, then the absolute sensitivity value increases from 4.8% to 23% respectively and for all cases, the absolute sensitivity remains independent of time (in terms of effective full power days) for a given value of βP and rises linearly with an increase in the value.

Joint DIII-D/EAST research on the development of a high poloidal beta scenario for the steady state missions of ITER and CFETR

Experimental and modeling investigations on the DIII-D and EAST tokamaks show the attractive transport and stability properties of fully noninductive, high poloidal-beta (βP) plasmas, and their suitability for steady-state operating scenarios in ITER and CFETR. A key feature of the high-βP regime is the large-radius (ρ > 0.6) internal transport barrier (ITB), often observed in all channels (ne, Te, Ti, rotation), and responsible for both excellent energy confinement quality and excellent stability properties. Experiments on DIII-D have shown that, with a large-radius ITB, very high βN and βP values (both ≥ 4) can be reached by taking advantage of the stabilizing effect of a nearby conducting wall. Synergistically, higher plasma pressure provides turbulence suppression by Shafranov shift, leading to ITB sustainment independent of the plasma rotation. Experiments on EAST have been used to assess the long pulse potential of the high-βP regime. Using RF-only heating and current drive, EAST achieved minute-long fully noninductive steady state H-mode operation with strike points on an ITER-like tungsten divertor. Improved confinement (relative to standard H-mode) and steady state ITB features are observed with a monotonic q-profile with qmin ∼ 1.5. Separately, experiments have shown that increasing the density in plasmas driven by lower hybrid wave broadens the q-profile, a technique that could enable a large radius ITB. These experimental results have been used to validate MHD, current drive, and turbulent transport models, and to project the high-βP regime to a burning plasma. These projections suggest the Shafranov shift alone will not suffice to provide improved confinement (over standard H-mode) without rotation and rotation shear. However, increasing the negative magnetic shear (higher q on axis) provides a similar turbulence suppression mechanism to Shafranov shift, and can help devices such as ITER and CFETR achieve their steady-state fusion goals.

Progress toward steady-state tokamak operation exploiting the high bootstrap current fraction regime

Recent DIII-D experiments have increased the normalized fusion performance of the high bootstrap current fraction tokamak regime toward reactor-relevant steady state operation. The experiments, conducted by a joint team of researchers from the DIII-D and EAST tokamaks, developed a fully noninductive scenario that could be extended on EAST to a demonstration of long pulse steady-state tokamak operation. Improved understanding of scenario stability has led to the achievement of very high values of βp and βN, despite strong internal transport barriers. Good confinement has been achieved with reduced toroidal rotation. These high βp plasmas challenge the energy transport understanding, especially in the electron energy channel. A new turbulent transport model, named TGLF-SAT1, has been developed which improves the transport prediction. Experiments extending results to long pulse on EAST, based on the physics basis developed at DIII-D, have been conducted. More investigations will be carried out on EAST with more additional auxiliary power to come online in the near term.

Particle optical properties at a Central Mediterranean site: Impact of advection routes and local meteorology

A multiwavelength integrating nephelometer and a PM10 sampler have been used to continuously measure optical properties and mass concentrations of particles at the ground level with the main aim of determining airflow and local meteorology effects on particle optical properties and PM10 mass concentrations. Measurements have been performed at Lecce (Italy), a coastal site in the Central Mediterranean and included scattering (σp) and hemispheric backscattering (βp) coefficients, and hemispheric backscattering fraction (βp/σp) at three wavelengths (450, 525, and 635nm), in addition to PM10 concentrations. The scattering Ångström exponent (å (λ1, λ2)) for different wavelength pairs (λ1, λ2), and the scattering Ångström exponent difference (∆å=å (450nm, 525nm)−å (525nm, 635nm)) have been calculated to estimate the airflow impact on the relative weight of fine and coarse mode particles. The yearly mean values±1 standard deviation of σp (450nm), βp (450nm), βp/σp (450nm), å (450, 635nm) and ∆å are equal to 100±50Mm−1, 12±6Mm−1, 0.13±0.02, 1.1±0.4, and 0.2±0.2, respectively. σp is well correlated to PM10 mass concentrations (r=0.96) and the PM10 mass scattering cross section is equal to 3.6±0.1m2g−1. The back trajectory cluster analysis has identified 5, 5, 7 and 7 distinct airflow types reaching the study site at 271, 500, 1500 and 3000m above the sea level, respectively, with only slight differences in airflow type among the four arrival heights. We have found that σp and βp values and their respective dependence on wavelength are strongly dependent on airflows. Therefore, we have shown that the in situ particle properties and the local meteorological parameters vary with advection routes. Given the dependence of å, ∆å, and βp/σp on particle size and shape, their strong association with airflows has indicated that the mean size distribution of sampled particles varies with air mass history and it has been shown that å, ∆å, and βp/σp values allow a satisfactory differentiation of the particle properties associated with different advection routes. More specifically, å and ∆å values have allowed distinguishing the airflows mainly responsible for the advection of fine mode particles from the ones which are mainly responsible for the advection of coarse mode particles. These results have provided a satisfactory understanding of the dependence on air flows of the mass scattering cross section values which vary from 2.9±0.2m2g−1 to 4.3±0.1m2g−1 with air flows. The airflow analysis has also allowed understanding the seasonality of the particle optical properties being linked to the airflow seasonality.

Hydrogen isotope effects on ITG scale length, pedestal and confinement in JT-60 H-mode plasmas

The dependence of heat transport, edge pedestal and confinement on isotopic composition was investigated in conventional H-mode plasmas. Identical profiles for the electron density, electron temperature and ion temperature were obtained for hydrogen and deuterium plasmas, whereas the required power clearly increased for hydrogen, which resulted in a reduction in heat diffusivity for deuterium. The determination of identical temperature profiles, despite the different heating power, suggested that the characteristics of heat conduction essentially differ for hydrogen and deuterium, even at the same scale length of temperature gradient. The self-regulating physics mechanism determining the overall H-mode confinement was also addressed. The inverse of the ion temperature gradient (ITG) scale length, or ∇Ti/Ti, which is required for a given ion heat diffusivity, increased by a factor of approximately 1.2 for deuterium compared with that for hydrogen. The relationship between edge pedestal pressure and global βp holds true consistently regardless of the difference in the isotopic composition. A higher value of βp was obtained for deuterium because of its smaller ITG scale length and because of the additional stored energy in the thermal and fast ion components, the latter due to an increase in the slowing down time with an increase in isotopic mass.

A scheme for finding the front boundary of an interplanetary magnetic cloud

Abstract. We develop a scheme for finding a "refined" front boundary-time (tB*) of an interplanetary magnetic cloud (MC) based on criteria that depend on the possible existence of any one or more of four specific solar wind features. The features that the program looks for, within ±2 h (i.e., the initial uncertainty interval) of a preliminarily estimated front boundary time, are: (1) a sufficiently large directional discontinuity in the interplanetary magnetic field (IMF), (2) a significant proton plasma beta (βP) drop, (3) a significant proton temperature drop, and (4) a marked increase in the IMF's intensity. Also we examine to see if the "MC-side" of the boundary has a MC-like value of βP. The scheme was tested using 5, 10, 15, and 20 min averages of the relevant physical quantities from WIND data, in order to find the optimum average to use. The 5 min average, initially based on analysis of N=26 carefully chosen MCs, turned out to be marginally the best average to use for our purposes. Other criteria, besides the four described above, such as the existence of a magnetic hole, plasma speed change, and/or field fluctuation level change, were examined and dismissed as not reliable enough, or usually associated with physical quantities that change too slowly around the boundary to be useful. The preliminarily estimated front boundary time, tB, and its initial ±2-h uncertainty interval are determined by either an automatic MC identification scheme or by visual inspection. The boundary-scheme was developed specifically for aiding in forecasting the strength and timing of a geomagnetic storm due to the passage of a MC in real-time, but can be used in post ground-data collection for imposing consistency when choosing front boundaries of MCs. This scheme has been extensively tested, first using 81 bona fide MCs, collected over about 8.6 years of WIND data (at 1 AU), and also by using 122 MC-like structures as defined by Lepping et al. (2005) over about the same period. Final statistical testing of the 81 MCs to see how close the refined boundary-time tB* lies with respect to a preliminary time tB(VI) was carried out, i.e., to find Δt1=(tB*–tB(VI)), for the full set of MCs, where tB(VI) is usually a very accurate time previously determined from visual inspection, This testing showed that 59 Δt1s (i.e., 73%) lie within ±30 min, 71 Δt1s (i.e., 88%) lie within ±45 min, and only 5 cases lie outside a |Δt1| of 1.0 h, which is only 6% of the full 81, and these 6% would be considered unsatisfactory. Since MC parameter fitting is usually done on the basis of 30 or 60 min averages, these results seem quite satisfactory. The program for this front boundary estimation scheme is located at the Website: http://wind.nasa.gov/mc/boundary.php.

Physical Interpretation of Flow and Heat Transfer in Preswirl Systems

This paper compares heat transfer measurements from a preswirl rotor–stator experiment with three-dimensional (3D) steady-state results from a commercial computational fluid dynamics (CFD) code. The measured distribution of Nusselt number on the rotor surface was obtained from a scaled model of a gas turbine rotor–stator system, where the flow structure is representative of that found in an engine. Computations were carried out using a coupled multigrid Reynolds-averaged Navier-Stokes (RANS) solver with a high Reynolds number k-ε∕k-ω turbulence model. Previous work has identified three parameters governing heat transfer: rotational Reynolds number (Reϕ), preswirl ratio (βp), and the turbulent flow parameter (λT). For this study rotational Reynolds numbers are in the range 0.8×106&lt;Reϕ&lt;1.2×106. The turbulent flow parameter and preswirl ratios varied between 0.12&lt;λT&lt;0.38 and 0.5&lt;βp&lt;1.5, which are comparable to values that occur in industrial gas turbines. Two performance parameters have been calculated: the adiabatic effectiveness for the system, Θb,ad, and the discharge coefficient for the receiver holes, CD. The computations show that, although Θb,ad increases monotonically as βp increases, there is a critical value of βp at which CD is a maximum. At high coolant flow rates, computations have predicted peaks in heat transfer at the radius of the preswirl nozzles. These were discovered during earlier experiments and are associated with the impingement of the preswirl flow on the rotor disk. At lower flow rates, the heat transfer is controlled by boundary-layer effects. The Nusselt number on the rotating disk increases as either Reϕ or λT increases, and is axisymmetric except in the region of the receiver holes, where significant two-dimensional variations are observed. The computed velocity field is used to explain the heat transfer distributions observed in the experiments. The regions of peak heat transfer around the receiver holes are a consequence of the route taken by the flow. Two routes have been identified: “direct,” whereby flow forms a stream tube between the inlet and outlet; and “indirect,” whereby flow mixes with the rotating core of fluid.

Diamagnetic measurement on HT-7 superconducting tokamak

Abstract Diamagnetic measurement is a basic diagnostics on tokamak. Some important plasma parameters such as plasma energy and betap βp can be obtained from this measurement. For most case, diamagnetic flux ΔΦ is extremely smaller than toroidal flux Φ (ΔΦ/Φ − 10−4). Therefore we have to use techniques that allow measurement to better than 1 part in 104 to get 10% accuracy in value of βp. Using a compensation coil is a typical technique to improve the signal to noise ratio. In this paper the design of diamagnetic diagnostics system for HT-7 superconducting tokamak device is introduced and some experimental results of plasma energy and βp are given in different plasma discharges.

Edge stability analysis of high βp plasmas

An MHD stability analysis of the edge plasma shows that in highly triangular plasmas, the increasing global βp has a stabilizing effect on the low-n instabilities that trigger edge localized modes (ELMs). The improved stability allows the access of higher edge pressure gradients before the ELM is triggered. At the same time, the edge plasma moves closer to the high-n ballooning mode stability boundary. The stability changes can explain why the high value of βp helps to access smaller ELMs.

Beta limit due to resistive tearing modes in T-10

Soft β limiting phenomena have been observed in T-10 in ECRH heatedplasmas. Neoclassical tearing modes are supposed to be responsible for the βlimitation. MHD onset was observed at high βp values but low βN values.The critical β has been found to be almost independent of the collisionality parameterνe*. Sawtooth stabilization by ECCD does not result in an increase of criticalbeta. A dependence of the critical β on the q(r) profile (modified by ECCD)has been observed.

Performance, heating and current drive scenarios of ASDEX Upgrade advanced tokamak discharges

Various approaches to high performance and steady state operation are presented. Strong neutral beam heating in the current ramp leads to internal transport barriers (ITBs) in conjunction with negative central magnetic shear. To avoid the destabilizationof external kink modes this regime is limited to L mode edge operation with βN < 1.7. In high poloidal β, βp, discharges, full non-inductive current drive has been achieved transiently. At Greenwald density, values of βp = 3.1, βN = 2.8 and HITER89-P = 1.8 have been reached simultaneously. In plasmas with ITBs and L mode edge, additional ECRH and ECCD facilitates high core confinement with Te ≈ Ti. CentralECCD has been applied in low density low current discharges. For ECCD in the co-current direction a current drive fraction of 82% is calculated. In the case of counter-ECCD, negative central shear withqmin > 1 leads to the formation of an electron ITB.

Nature, properties, and origin of low‐frequency waves from an oblique shock to the inner magnetosheath

We analyze the high time‐resolution profiles of the electron density and of the magnetic field and the plasma parameters recorded by ISEE 1 and 2 during a crossing of the Earth's magnetosheath at 1430 LT. Compressive and Alfvén ion cyclotron modes (AIC modes) are identified by comparing the measured magnetic polarization and electron parallel compressibility with the results of calculations in an unstable kinetic linear model. A criterion to discuss the accuracy of the wave vector direction of mirror modes is established; an efficient method to disentangle mirror and AIC modes is presented and applied. From the bow shock to the inner sheath we identify successively (1) compressive modes and AIC modes in the oblique shock, (2) a pure AIC mode region of circularly and elliptically polarized waves in a layer 0.3 RE thick adjacent to the undershoot, (3) a mixed region 2 RE thick where both mirror modes and AIC modes are observed, (4) a pure mirror mode region. The nature of the dominant mode appears to be controlled by the depth in the magnetosheath, more than by the local values of βp and the proton temperature anisotropy Tp⊥/Tp‖. In the outer sheath the unusual identification of a pure Alfvénic region for a large average proton beta βp = 13 and a moderate proton temperature anisotropy could be explained by a relatively low density of α particles. The mirror modes are three‐dimensional structures with their major axis along the magnetic field and with their minor axis nearly perpendicular to the magnetopause surface. We estimate the dimensions of ordered structures observed in the middle of the magnetosheath for a βp around 7 ± 1 and Tp⊥/Tp‖ around 1.5; the minor axis of regular mirror modes is typically between 1300 and 1900 km long; the intermediate dimension is larger than either 2200 or 2700 km, while the major axis is larger than either 2700 or 3400 km. For the first time the measured parallel compressibility of the pure mirror modes is shown to be in relatively good agreement with the linear model predictions for 4 &lt; βp &lt; 11. The absence of AIC modes in the inner sheath suggests that these modes cannot grow or propagate in regions where mirror modes are well developed and that AIC wave energy is not transferred across a large‐amplitude mirror mode region.

Physical mechanism of enhanced stability from negative shear in tokamaks: Implications for edge transport and the L-H transition

The enhancement of stability to ballooning modes from negative shear in tokamaks is shown to be a simple consequence of the orientation of the convective cell with respect to the toroidally outward effective gravity, g↘. For modest positive shear, convective cells remain oriented along g↘ as they map along field lines. In contrast, for negative shear or very positive shear convective cells twist strongly away from g↘ and are less strongly driven. The twist of convection cells is controlled by the profile of the vertical magnetic field along the outer midplane, Bz. Twist is a minimum in regions where Bz is independent of the major radius. Transport should be highest in such locations. Resistive ballooning modes in the tokamak edge are strongly stabilized by modest values of negative shear. Tokamak discharges with finite values of βp develop regions of local negative shear on the outside midplane of the plasma torus. This local negative shear should self-stabilize resistive ballooning modes at finite values of the poloidal beta. This effect may impact the transition to high confinement operation (H-mode).

A model for ideal m=1 internal kink stabilization by minority ion cyclotron resonant heating

A generalized energy principle is used to determine the effect of ion cyclotron resonant heating (ICRH) on the stability of m=1 internal kink displacements in the low-frequency limit: such displacements are associated with sawtooth oscillations. An integral expression is obtained for the contribution to the plasma energy of an ICRH-heated minority ion population with strong temperature anisotropy, which relates the former to the ICRH power input and its deposition profile. The link is provided by a realistic, but analytically tractable, new model for the distribution function of the heated ions, which is based on the approach of Stix [Nucl. Fusion 15, 737 (1975)]. Numerical evaluation of the integral expression is carried out using parameters inferred from ICRH experiments in the Joint European Torus (JET) [Campbell et al., Phys. Rev. Lett. 60, 2148 (1988)]. It is shown that the ideal m=1 internal kink is stable at values of the poloidal plasma beta βp which typically lie in the range 0.4–1, depending on the radio-frequency power input and the radius r1 of the q=1 surface. Stability is thus possible at values of βp lying significantly above the magnetohydrodynamic instability threshold (≂0.3). If the perpendicular temperature T⊥ of the hot ions exceeds the parallel temperature by a factor of 10 or more, and r1 is greater than about one-third of the plasma minor radius, trapped ions have a greater stabilizing effect than passing ions. Stabilization is most easily achieved, however, if r1 is small. The hot-ion plasma energy depends strongly on the value of T⊥, but for fixed T⊥ is insensitive to the degree of anisotropy.

Non-inductively current driven H mode with high beta N and high beta p values in JT-60U

Attainable βp and βN values were widely improved in JT-60U by peaking of the current profile and broadening of the pressure profile. In a quasi-steady state of ELMyy H mode, βp approximately 2.5-3, βN approximately 2.5-3.1 and H factor approximately 1.8-2.2 were sustained for approximately 1 s simultaneously under the full current drive condition (bootstrap current 60%, beam driven current 48% at Ip = 0.5 MA). In a transient case, the maximum values of βp, ϵβp and βN reached 4.7, 1.2 and 4.2, respectively. The achievable βp value increases systematically with safety factor at the edge. To obtain these improved high β plasmas, it is essential to control MHD activities; suppression of βp collapse and medium m/n (poloidal mode number/toroidal mode number) modes by the modification in current and pressure profiles and control of ELM activity by suitable selection of the heating power

ChemInform Abstract: The Hydrolysis of Azetidinyl Amidinium Salts. Part 2. Substituent Effects, Buffer Catalysis and the Reaction Mechanism

The hydrolysis of azetidin-2-ylideneammonium salts gives a mixture of β-lactams, by exocyclic C–N bond fission, and β-amino amides, by endocyclic C–N bond breakage and opening of the four-membered ring. The reaction is general-base catalysed and more β-lactam is formed using a less basic buffer. The mechanism of the buffer-catalysed reaction is the general-acid-catalysed breakdown of a reversibly formed neutral tetrahedral intermediate. The Bronsted α-values vary with substituents in the amidinium salt so that they decrease with increasing electron withdrawal in the nitrogen amine which is expelled. Electron-withdrawing substituents attached to either nitrogen of the amidinium salt favour expulsion of that leaving-group amine. The Bronsted β1g for endocyclic C–N bond fission and β-amino amide formation is –0.52 whereas that for exocyclic C–N bond fission and β-lactam formation is –0.83. Substituent effects on the nitrogen amine which is not expelled but forms the product amide or β-lactam generate βp values of –0.71 and –0.07, respectively. Changes in structure–reactivity relationships with substituents are examined by an analysis of the reaction mechanism.

The hydrolysis of azetidinyl amidinium salts. Part 2. Substituent effects, buffer catalysis, and the reaction mechanism

The hydrolysis of azetidin-2-ylideneammonium salts gives a mixture of β-lactams, by exocyclic C–N bond fission, and β-amino amides, by endocyclic C–N bond breakage and opening of the four-membered ring. The reaction is general-base catalysed and more β-lactam is formed using a less basic buffer. The mechanism of the buffer-catalysed reaction is the general-acid-catalysed breakdown of a reversibly formed neutral tetrahedral intermediate. The Bronsted α-values vary with substituents in the amidinium salt so that they decrease with increasing electron withdrawal in the nitrogen amine which is expelled. Electron-withdrawing substituents attached to either nitrogen of the amidinium salt favour expulsion of that leaving-group amine. The Bronsted β1g for endocyclic C–N bond fission and β-amino amide formation is –0.52 whereas that for exocyclic C–N bond fission and β-lactam formation is –0.83. Substituent effects on the nitrogen amine which is not expelled but forms the product amide or β-lactam generate βp values of –0.71 and –0.07, respectively. Changes in structure–reactivity relationships with substituents are examined by an analysis of the reaction mechanism.

MHD stability properties of bean-shaped tokamaks

A study of the MHD stability properties of bean-shaped tokamak plasmas is presented. For ballooning modes, while increased indentation gives larger stable-beta configurations, the existence and accessibility of the second stable region are sensitive to the pressure and safety factor profiles. The second stable region appears at lower beta values for large aspect ratio and moderately high q-values. Finite-Larmor-radius kinetic effects can significantly improve the stability properties. For low-q (⪅ 1) operation, long-wavelength (n ∼ 2, 3) internal-pressure-driven modes occur at modest βp values and accessibility to higher beta operation is unlikely. Indentation modifies the nature of the usually vertical axisymmetric instability, but the mode can be passively stabilized by placing highly conducting plates near the tips of the plasma bean. At constant q, indentation has a stabilizing effect on tearing modes.