Role of magnetohydrodynamic activity in sawtooth induced heat pulse propagation in ADITYA tokamak

Fast propagation of sawtooth induced heat pulse is observed in the magnetohydrodynamic (MHD) active plasmas of ADITYA tokamak. The sawtooth crash deposits heat beyond the inversion radius, which gets transported to the edge region of the plasma, and is reflected as inverted sawtooth modulation in the edge channels of electron cyclotron emission (ECE) and Hα spectral line emission. The time-lag analysis on ECE signal reveals the propagation time from plasma core to edge of ∼150 µs. From this analysis, the estimated transient electron heat diffusivity χehp is found to be ∼50–60 m2 s−1, which is ten times higher than that of power balance heat diffusivity χepb , in the MHD active discharges of ADITYA. It has been observed that the presence of MHD (m/n = 2/1, 3/1) activity in the intermediate region between the q = 1 and the edge radii, significantly influences the heat transport from the plasma core to the edge region. Stochastic magnetic field region formation with overlapping m/n = 2/1 and 3/1 MHD islands facilitates the fast heat-pulse propagation during a sawtooth crash in ADITYA tokamak. The disparity between the measured and the power-balance estimated diffusivity is significantly reduced by considering the electron heat diffusivity due to stochastization of magnetic field in the intermediate region.


Introduction
To optimize and quantify the operating scenario of fusion devices for achieving well confined burning plasma, better understanding of the electron heat transport is required. Over * Author to whom any correspondence should be addressed.
Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. the years, it has been established that the electron heat transport is primarily driven by turbulent transport, when the temperature gradient exceeds a threshold value [1]. Various experimental and theoretical studies have shown that trapped electron mode (TEM), electron temperature gradient (ETG) and ion temperature gradient (ITG) modes are mainly responsible for turbulent driven heat transport [1]. It is generally believed that the magnetic fluctuations do not influence the energy transport in tokamaks. However, there are ample examples of magnetic fluctuations facilitating the electron heat transport in tokamaks [2,3]. It has also been observed that the heat transport parallel and perpendicular to the magnetic field lines differs significantly. Due to the difference in heat diffusivity parallel and perpendicular to the magnetic field lines, the heat transport becomes very sensitive to changes in magnetic field topology [2,4]. Besides, steady-state heat transport, transient heat transport events like impurity injected cold pulse propagation, sawtooth crash induced heat propagation and electron cyclotron heating (ECH) modulation, are also known to be significantly influenced by the magnetic fluctuations and magnetic island formations in tokamaks [1,4,5].
Furthermore, the transient heat transport in tokamaks is found to have large electron heat diffusivity as compared to those estimated from the power balance calculations [4]. In Axially Symmetric Divertor Experiment-Upgrade (ASDEX-U), ECH power modulated transient electron heat transport in low density plasmas is explained invoking the presence of TEMs [6]. Similarly, many features of the impurity induced cold pulse propagation is explained using trapped gyro Landau fluid quasilinear transport model in the ALCATOR C-Mod [5]. But, in case of sawtooth-induced heat pulse propagation, a clear understanding of underlying mechanism still requires attention in terms of how the magnetic topology influence electron heat transport in the intermediate region between the q = 1 surface and the plasma edge. The heat diffusivities in the aftermath of a sawtooth-crash event may quite differ from those observed in other transient phenomena, because, the sawtooth of sufficient period length can even trigger a tearing mode or enhance width of existing tearing mode island resulting the alteration of magnetic topology of plasma in the intermediate region [7][8][9]. And, thereby the heat pulse propagation induced by a sawtooth-crash event in presence of a magnetic island or a stochastic magnetic field region gets significantly modified. Such observations have been reported in TJ-II [10], DIII-D [11] and simulation studies in tokamak geometry [12]. These studies clearly indicate the role of magnetic topology in the turbulent heat transport processes.
The investigation of sawtooth induced heat pulse propagation and using it for estimating electron heat diffusivity in tokamak devices started long ago, first observed in the Oak Ridge Tokamak (ORMAK) device [13]. The sawtooth instability provides the source of heat perturbation and the fast sawtooth crash deposits heat beyond the inversion radius (q = 1 surface). This deposited heat gets transported towards the edge region and the nature of transport is diffusive. Thus, fast crash phase is accompanied by the heating of the edge plasma. Based on this assumption, diffusive transport of heat beyond the inversion radius has been widely used to understand and test the theoretical models for the transport of heat in tokamak devices. However, the electron heat diffusivity for the sawtooth induced heat pulse has been found to be much higher, by a factor of 2.5-15 than that implied by the power balance estimate. To explain this, it has been suggested that either this is a feature of observing only high energy electrons, or that the pulse transport is influenced by the sawtooth crash mechanism itself [13]. Moreover, the observations in the ORMAK suggested that with increase in radii of the q = 1 resonant surface at the time of sawtooth crash, heat pulse propagation becomes progressively faster with shorter time delays, until the χ hp e increases by a factor of four or more for the successive heat pulse [13].
Similar study has been carried out in the Tokamak Fusion Test Reactor (TFTR) tokamak [14]. The result showed that time lag ∆t p is proportional to ∆r 2 , indicating diffusive nature of the heat pulse transport. However, the electron heat diffusivity χ hp e characterizing the sawtooth induced heat perturbation has been found to exceed the electron heat diffusivity χ pb e for the background plasma determined from power balance consideration. This study revealed two more important features, the heat deposited well beyond the reconnection radius on a very short time scale, within 200 µs following the sawtooth crash, and the presence of helical distortion outside the q = 1 surface, well beyond mixing radius during the final phase of the sawtooth precursor. The presence of m = 1 helical distortion produced magnetic field stochastization and hence resulted in enhancement of the electron thermal diffusivity χ hp e by factor of 40 in short time duration of 1 ms. An estimation of mixing radius has the ranges between 40% and 50% of minor radius, a for moderately high β T plasmas. But in case of Ohmic plasmas, mixing radius may not extent to such a large fraction of minor radius [14].
The comparative study in the DIII-D and TFTR tokamaks [15], showed that the sawtooth induced heat pulse propagated beyond the inversion radius and displayed diffusive nature of transport, with electron heat diffusivity χ hp = 10χ pb . While, in the same plasma condition, partial sawtooth-crash induced heat perturbation propagated with thermal diffusivity values equal to those estimated using power balance estimate. Similar observation has also reported in ALCATOR-C mod tokamak. The relatively slow propagation of partial sawtooth-crash induced heat pulse propagation has been used to obtain the electron heat diffusivity χ e in equilibrium condition, is in good agreement with the power balance estimates [16]. These observations indicated that, the propagation of sawtooth induced heat pulse may be the property of the sawtooth crash itself, and not be due to enhanced nonlinear transport [15]. The fast propagation of heat pulses are also reported in the TJ-II stellarator [17] and the Joint European Torus (JET) tokamak [18], but with limited explanations regarding the underlying mechanisms.
Although, the sawtooth-induced heat pulse is studied in detail in different tokamaks, the disparity between the experimentally measured electron heat diffusivity with those estimated using the power balance calculation remains unexplained. In the reported studies, the experimentally measured thermal diffusivity, χ hp e has always been found to be higher by factor of two to ten then that of the thermal diffusivity estimated from the power balance calculations, χ pb e . The measured fast propagation of heat pulse with relatively higher heat diffusivity has been termed as the 'ballistic effect' [14]. To explain this fast propagation of the sawtooth induced heat pulse, several physical models are proposed invoking the role of stochastic magnetic field in region near to inversion radius [13][14][15]19], the energetic particle effect [13], the coupling of electron temperature and density [20,21], turbulence spreading [22] and the electrostatic turbulence [23]. But, the role of magneto-hydrodynamic (MHD) activity in the intermediate confinement region between the mixing radius and plasma edge in the fast propagation of heat-pulse has not been investigated systematically. These MHD modes in confinement region can couple with the kink mode at the time of sawtooth crash instantaneously and provide channel for heat transport [24]. Dependency of magnitude of electron heat diffusivity on single and multiple overlapping magnetic islands formation has also been reported [25,26]. The controlled experiments using modulated Electron Cyclotron Resonance Heating (ECRH) heating in plasma core for thermal diffusivity profile measurement have shown that the presence of stochastic magnetic field enhanced the electron heat diffusivity [27].
In the ADITYA tokamak, clear evidence of the role of MHD (m/n = 2/1, 3/1) activity in fast propagation of sawtooth induced heat pulse propagation is observed in the intermediate plasma region, i.e. in the region between q = 1 resonant surface, (sawtooth crash event location) and the plasma edge. The measured time-lag between the electron-cyclotron (EC) emissions from the core and edge region, following a sawtoothcrash gives the heat pulse propagation time. A sawtoothcrash event deposits heat beyond the inversion radius, which gets transported to the edge region of the plasma and manifests as observations of inverted-sawtooth modulation in the edge channels of EC emissions and H α spectral line emission intensity. In number of discharges, it has been found that, inverted sawtooth in H α signal appears only when MHD activity is strong, indicating an influence of MHD activity on the heat-pulse propagation. The time-lags are observed in the range of ∼150-200 µs corresponding to transient electron heat diffusivity χ hp e in the range of ∼50-60 m 2 s −1 in many plasma discharges with strong MHD activity and 35-40 m 2 s −1 in discharges with relatively weak MHD activity. Whereas, the estimated heat diffusivity using the power balance calculations for the analysed discharges comes out to be ∼6 m 2 s −1 . The fast and slow propagation of sawtooth-crash triggered heat pulse events are also observed in solitary discharges where the magnitude of the MHD activity varies during the discharge. This observed disparity between the sawtooth induced transient electron heat and power balance diffusivity in the MHD active plasmas of ADITYA can be reconciled to large extent by taking into account the heat diffusivity induced by the stochastization of magnetic field due to overlapping of m/n = 2/1 and 3/1 magnetic islands, along with the turbulence driven heat diffusivity. The experimental observations and analysis clearly suggest that the sawtooth-induced heat-transport is significantly influenced by the presence of MHD (m/n = 2/1, 3/1) activity in the intermediate plasma region of ADITYA tokamak discharges and helps in resolving the ambiguity between the measured and power-balance estimates of heat-diffusivity to a large extent.
The article is arranged as follows, the section 2 gives the details of experimental setup, section 3 presents experimental results and analysis, section 4 elaborately discusses the experimental findings and finally section 5 concludes the study.

Experimental setup
The ADITYA [28] is a mid-size limiter tokamak with major (R) and minor (a) radius of 0.75 m and 0.25 m, respectively. It has a stainless-steel vacuum vessel with rectangular cross section and graphite poloidal limiter at one toroidal location. The plasma parameters during this experimental campaign are, toroidal magnetic field B T ∼ 0.75-1.0 T, plasma current I p ∼ 80-100 kA, line averaged plasma electron densityn e ∼ 0.8 − 1.8 × 10 19 m −3 , and core electron temperature T e ∼ 200 − 350 eV. The edge safety factor q a is ∼4.5 during flat-top phase of the plasma current.
The MHD activity is measured by a set of 15 Mirnov coils located at the poloidal periphery with equal angular separation at one toroidal location. These Mirnov probes are placed at r = 26.5 cm, 1.5 cm outside the limiter and have a linear frequency response up to 40 kHz. The plasma density and its radial profile is measured by seven channels fixed-frequency O-mode, 100 GHz microwave interferometer covering entire plasma cross-section [29]. Soft x-ray (SXR) emission from the ADITYA tokamak is detected using a pin-hole camera, which consist of an array of six surface barrier diode (ORTEC made, active area ∼50 square mm, thickness ∼100 mm) detector. This pinhole camera measurement is also used to estimate electron temperature by foil absorption technique using two Beryllium foils having different thicknesses. The Langmuir probes are used for floating potential measurement in these plasma discharges. The Langmuir probe is made up of molybdenum pin with dimension 1 mm diameter and 5 mm long. The Langmuir probe measurement is carried out at 1 MHz sampling rate during 40-64 ms time period of the discharge [30]. The H α (λ = 656.28 nm) spectral line emission from the neutral hydrogen is monitored using photo-multiplier tube with interference filter from three different lines of sight terminating on inboard, outboard and top limiter tiles [30]. To obtain the MHD structure and to estimate the island width, Mirnov coil signal are analysed using singular value decomposition (SVD) technique in form of the eigenvector associated with each mode, along their eigenvalues [31]. The electron cyclotron emission (ECE) measurement uses two radiometers, E-band (60-90 GHz) and Ka-band (27-39 GHz) for third harmonic and second harmonic cyclotron radiation measurements respectively [32]. The ECE, H α and electron density measurements are sampled at 125 kHz, while the Mirnov and SXR signal are acquired with a sampling rate of 100 kHz. All data are acquired using computer automated measurement and control (CAMAC) based data acquisition system.

Experimental observations
The temporal evolution of a typical ADITYA tokamak plasma discharge #14139, with loop voltage (V), plasma current (kA), SXR signal (a.u.), Mirnov oscillationḂ p (a.u.) and H α spectral line emission (a.u.) is shown in figures 1(a)-(e) respectively. The magnitude of loop voltage during flat-top phase is about 2-3 V and plasma current is about 75 kA. The sawtooth activity begins to appear at ∼40 ms in the discharge and remains active till the end of the discharge. The three line of sight of for the H α spectral line emission measurement are terminated on the inboard, outboard and top limiter tiles. The inverted sawtooth structure is clearly visible in the H α emission signal, but this feature in H α is more prominent in the presence of stronger MHD activity as depicted in figure 1(d). The observed sawtooth period is around 700 µs and sawtooth crash time is 60-80 µ s. The inversion radius is ∼6 cm, derived from the experimental observations [33]. It has generally been observed that sawteeth are in the collisionless regime with a faster reconnection rate observed in large tokamaks [34]. However, the observed sawtooth crash time in ADITYA of ∼60-80 µs matches quite well with the Kodomstev (Sweet-Parker) With the core electron temperature ∼300-500 eV, B T = 0.76 T and density 1-2 × 10 19 m −3 in ADITYA, the resistive diffusion time, τ R = r 2 c µ 0 η ∼ 30 ms and the Alfven time, radius of the q = 1 surface and other symbols having their standard meaning [34]. The figure 2(a:1-3) shows that, in presence of considerable MHD activity, inverted sawtooth observed in the H α emission corresponding to every sawtooth crash in the SXR signal. The Mirnov signal is having higher magnitude and shows periodic behaviour along with sawtooth activity. While, with relative decrease in the MHD activity as depicted in figure 2(b:2), inverted sawtooth in the H α signal ceases to appear as seen in figure 2(b:3). This result is indicative of how MHD activity influencing the heat transport from the plasma core to edge region. It may so happen that, in presence of strong MHD activity, heat transport may get enhanced, while with weak MHD activity, it may not affect the electron heat diffusivity significantly. Such experimental observations with inverted sawtooth in visible spectral emission as a result of sawtooth crash in the plasma core has been reported in JET [35] and HT-7 [36], but the role of MHD activity in electron heat transport remained less explored.
The is appearing due to the sawtooth activity in the plasma. Also, frequency of MHD (m/n = 2/1, 3/1) modes in the frequency range of 10-15 kHz is clearly visible. The finger-like structure in SXR signal is visible after at every sawtooth crash as shown in figure 3(a-1).
The sawtooth activity is also observed in the ECE signals, and these are used to track the temporal and spatial evolution of sawtooth induced heat pulse propagation. Figure 4 shows the ECE signal from different radial locations, ρ = 0.24, 0.36, 0.52, 0.72 and 0.92 respectively. Here, the data from shot #13262 is presented, which is almost similar to shot #14139, as in the later discharge, one of the ECE channel was not properly working. The measurement is carried out on the low field side. The ECE diagnostic has sufficient time resolution of ∼8 µs to resolve and track the fast propagation of heat perturbation from core to edge region of plasma. One can see, modulation is having fast rise and slow fall resembling inverted sawtooth appearing at the radial location of ρ = 0.92. This is similar to the modulation seen in the H α signal confirming the heat pulse propagation to the edge during the sawtooth activity.
The dominant MHD modes present in the plasma is determined by applying SVD technique on array of Mirnov coil signal [31]. We find the presence of two modes, m/n = 2/1 and 3/1. The poloidal mode structure of 2/1 and 3/1 MHD modes are shown in figures 5(a) and (b), respectively. The island width of a MHD island associated with mode structure can be calculated using following formula [37,38], where w is the island width, m is the poloidal mode number, r s is the radius of the resonant mode surface, r c is the radius of Mirnov coil location, B p is the fluctuations in the poloidal magnetic field and B p is the poloidal magnetic field. The location r s for the mode's m/n = 2/1 and 3/1 are 14 and 19 cm, respectively. The calculated island width during sawtooth activity for m/n = 2/1 and 3/1 mode are shown in figure 6. It can be seen that, just after sawtooth crash, indicated by the vertical line in the figure, island widths of both 2/1 and 3/1 modes increase. The increments in island widths are ∼6-7 cm and 4.5-5.0 cm for 2/1 and 3/1 MHD modes, respectively.

Estimation of electron heat diffusivity
The time-lag analysis has been carried out on the signals from different radial locations of the ECE measurement, which is tracking the propagation of heat perturbation from the plasma core to edge region. This analysis gives better idea of underlying mechanism responsible for the fast propagation of sawtooth induced heat pulse. This is done by comparing the sawtooth induced heat transport time scale with the standard time scales in tokamak plasma, such as Bohm diffusion time and Alfven time etc as mentioned in section 3.1. Moreover, an approximate estimation of effective heat diffusivity χ hp e can also be made. The time-lag between the SXR and H α signals, shown in figure 2, is observed to be ∼200 µs, whereas timelag between central ECE at ρ = 0.24 and edge at ρ = 0.92 is ∼150 µs. This difference in time-lags obtained from two measurements is related to different radial locations of the diagnostics. The SXR central chord is passing through the plasma centre, ρ = 0.0, but the radial location of ECE central chord is ρ = 0.24. Consequently, the estimation of time-lag using ECE channels lead to lower value. However, the use of ECE diagnostic is more prudent as the pilling effect, which is normally observed in the case of line integrated SXR radiation measurement, can be avoided. Figure 5 shows the plot of timelag between successive ECE channels versus the square of the corresponding radial location for both the shots # 13262 and 14139.
Before proceeding with the estimation of electron heat diffusivity from the data presented in figure 7, we here briefly describe the theoretical background for analysing the sawtooth   induced heat pulse perturbation for estimating the electron heat diffusivity, which has been used in many experimental studies [13][14][15][16][17]19]. The detailed discussion can be found in [13,19]. The mathematical description of the heat pulse propagation is given by Callen and Jahns [13], starting with the general electron heat balance equation [19], ∂T e (r, t) ∂r + Q (2) where Q is the electron heat source and sink term, which includes Ohmic heating, collisional heat transfer to ion, convection, radiation and auxiliary heating terms and χ hp e is electron heat diffusivity. A small sawtooth induced temperature perturbationT e (r, t) in a near equilibrium situation is governed by the following equation, The equation (3) is derived by applying perturbation to equation (2) and neglecting the additional term of heat sink/ source, because the equilibrium implied by this term is slow and broadly distributed compare to the highly localized, both in space and time, perturbation induced by the sawtooth. The analytical solution of equation (3) with appropriate initial condition can be given by sum of two opposite delta functions of temperature perturbation; one for inside the inversion radius and other outside of that. As described in [13], under the longtime asymptotic limit, the solution of equation (3) lead to the time of maximum temperature perturbation at a given plasma radius. This maximum time t p at which the peak ofT e occurs, is estimated to be ∆t p = ∆r 2 / 9χ hp e , applicable in confinement region (1.7 < r/r s < 5), where r s is the inversion radius. Hence, when experimental data with the change in time-lag t p versus increase in r 2 is plotted, the data should fall on straight line whose slope is equal to 1/9χ hp e . In the theoretical treatment described above, it is assumed that, the electron density n e and electron heat diffusivity χ hp e are constant over minor radius. In reality, there is a spatial variation in electron density and electron heat diffusivity. To justify these assumptions, detailed sensitivity study has been carried out in [19] by considering both constant and different radial profiles of electron density n e and electron heat diffusivity χ hp e respectively. The strong radial localization of the perturbation and the 'weak' logarithmic dependence on n e (r), particularly for decreasing n e as radius increases, the solution depends weakly on the density profile n e (r). While, if one considers radial dependence of the electron heat diffusivity χ hp e (r), there would be significant deviation from the experimental data points from the straight-line fit. However, in our case, the experimental data points are falling near to linear fit within the error bar of 10% as shown in figure 7. This indicates weak radial dependence of electron heat diffusivity in the present case. Hence, above assumption of considering constant values in radius are well justified and comply within the experimental uncertainty and are having non-significant impact on the final results obtained.
As shown in figure 7, the linear fit to experimental data points gives the slope equal to 0.19 µs cm −2 . Equating this slope with 1/9χ hp e , we have the estimation of effective electron heat diffusivity χ hp e ∼ 50-60 m 2 s −1 for plasma discharge with relatively strong MHD (m/n = 2/1, 3/1) activity. Whereas, in a discharge having relatively weak MHD activity (shot #14176), we find electron heat diffusivity is about 35-40 m 2 s −1 . This result clearly indicates influence of MHD (m/n = 2/1, 3/1) activity in the intermediate region on electron heat transport. While, electron heat diffusivity estimated from the power balance assumption using formula χ pb e ∼ a 2 /4τ E [13] is about 6 m 2 s −1 , where a is minor radius and τ E energy confinement time, is taken to be ∼5 ms. The effective electron heat diffusivity derived from time-lag analysis of heat pulse propagation is found to be larger by a factor of 10 as compared to the estimation using power balance calculation, χ hp e ∼ 10χ pb e for the MHD (m/n = 2/1, 3/1) activity plasmas of ADITYA. The obtained χ hp e of ADITYA tokamak has been compared with the values found in other tokamaks obtained by carrying out similar exercise. The χ hp e values are estimated to be 2.5-15 χ pb e in ORMAK [13], χ hp e ∼ 5χ pb e in TFTR, χ hp e ∼ 10χ pb e in DIII-D [15], and χ hp e ∼ 2 − 4χ pb e in JET [18]. To summarize, all observations, the χ hp e exceeds by factors ranging from 2.5 to 15χ pb e depending on machines and their operating regime. In the following, we compare the estimated heat pulse propagation time with standard time scales, for the typical ADITYA plasma parameters of, electron density n e ∼ 1.6 × 10 19 m −3 , electron temperature kT e = 300 eV, safety factor at the axis q 0 = 0.9 , minor radius a = 0.25 m and toroidal magnetic field B T = 0.8 T. The resistive diffusive time τ R is ∼ µ0rs η ∼ 30 ms, Bohm diffusion time a 2 ( 1 16

KTe B T
) is

∼2.6 ms and Alfven time τ
is the inversion radius, η is the resistivity, R is the major radius, q 0 is the centre safety factor, B T is the toroidal magnetic field and ρ is the mass density. The observed time scale of sawtooth induced heat pulse propagation is fast enough compared to turbulent time and resistive diffusion time scale, while it is slow compared to Alfven time scale. So, this heat pulse propagation time scale does not fall near to any of the above calculated time scales.

Discussion
The important result obtained through the analysis of sawtooth modulation observed in H α and ECE signal in ADITYA, is the time required for heat perturbation to reach the plasma edge region is around 200 µs, which is around three times that of sawtooth crash time. The inverted sawtooth modulation in the plasma edge emissions is only observed when there a presence of MHD (m/n = 2/1, 3/1) activity in the intermediate region following a sawtooth crash. This observation indicates fast propagation of heat pulse in the confinement region between q = 1 resonant surface and plasma edge is significantly aided by the MHD (m/n = 2/1, 3/1) phenomenon in the intermediate region following a sawtooth crash event. The formation of stochastic magnetic field due to the overlapping of m/n = 2/1, 3/1 islands in the intermediate region is found to enhance the electron heat diffusivity, and hence it could be one of the mechanisms that may explain fast propagation of sawtooth induced heat pulse in ADITYA. Whereas, the corresponding heat diffusivity calculated using the power balance estimates i.e. χ pb e ∼ a 2 4τE , is smaller by a factor of 10 compared to the measured heat diffusivity.
As no modulation in the line averaged electron density measured along a chord passing through the plasma centre is observed during the sawtooth crash in the analysed discharges, the coupling of temperature-density does not seem to be affecting the heat transport in our discharges. Figure 8 shows the sawtooth in SXR signal, central chord plasma density, inverted sawtooth in ECE (ρ = 0.92) signal and H α emission from the plasma shot #13262. It can be seen from figure 8(b) that the plasma density does not display any sign of sawtooth modulation. Note that the microwave interferometer diagnostic is capable of measuring the density fluctuation down to 2 × 10 18 m −3 [39]. Hence, in present case, if any density modulation exists, it may be either below the detectable limit of the diagnostic or else it might have insignificant contribution to the sawtooth oscillation. In some discharges of ADITYA tokamak, other than the discharges considered here, shows the sawtooth modulation in density, but their strength is very small, is ∼2% of plasma density n e [39]. Considering almost miniscule presence of sawtooth activity in some and no apparent sawtooth activity in density signal of the analysed discharges, it can be said that the sawtooth oscillation on the SXR emission signal is caused predominantly by the change in the electron temperature in the plasma core. This observation indicates that the conductive term contributes mainly to the heat transport.
As seen in the experimental studies of Texas Experimental Tokamak (TEXT) tokamak [21], transport induced by electrostatic fluctuation has a role in sawtooth induced fast heat propagation. Here, a sawtooth signature in floating potential was observed and the electrostatic fluctuation level modified reasonably. This modification of floating potential along with plasma density was found to increase the heat and particle fluxes in the plasma edge. In ADITYA tokamak, floating potential V F measured using Langmuir probe in the edge region of plasma during the sawtooth activity in the shot #14069 is shown in figure 9(b). This discharge is chosen as  the Langmuir probe measurements was not available in the shots, #13262 and #14139. The continuous wavelet transform of floating potential signal plotted in figure 9(c), shows that the electrostatic fluctuation has not been observed altering drastically during the sawtooth activity in ADITYA tokamak.
The MHD collapse event are known to generate turbulence and heat avalanche events [22]. These turbulence and heat pulse are observed to be propagating to the peripheral region faster than the diffusion time scales, with the turbulence preceding the heat pulse. This turbulence spreading, the propagation of turbulent fluctuation into different regions by nonlinear spectral transfer, is considered to be one of the mechanisms explaining the fast non-local heat transport. The turbulence spreading is modelled theoretically using a reactiondiffusion equation (Fisher-Kolmogorov-Petrovsky-Piskunov equation) [22,40]. The models suggest that a turbulence front propagates ballistically at a speed of V ≈ (γD) 1/2 , where γ is the local turbulence growth rate and D is the local mean turbulent diffusivity. Taking γ ≈ v Thi /a and D as gyro-Bohm where v Thi is the ion thermal velocity, a is the minor radius, and ρ s is the ion gyro radius [22,40]. However, it has been reported that the model estimated velocity of turbulence spreading matches well with the heat pulse propagation. Whereas, the measured speed of turbulence spreading has been found to be an order faster than that estimated using the above model calculations.
Considering the typical ADITYA parameters, toroidal magnetic field B T = 0.8 T, kT i = 100 eV, minor radius a = 0.25 m, the ρ s ∼ 1.2 × 10 −3 m, v Thi ∼ 10 5 m s −1 gives the propagation speed V ∼ 500 m s −1 . Which is quite close to observed heat pulse propagation velocity due to sawtooth crash in our experiments. However, in our experiments, we have observed that the heat pulse propagation velocities due to sawtooth crashes of similar magnitudes differ significantly. This has been observed to be happening due the presence and absence of MHD activity corresponding to m/n = 2/1 and 3/1 in the intermediate region between q = 1 surface and the edge. Furthermore, although the turbulent front propagation speed is in fair agreement with the sawtooth-induced heat pulse propagation velocity, there is no observation of any variation of density fluctuations due to the sawtooth crash. There is no signature of any change in the fluctuation magnitudes in any of the microwave interferometry channels following the sawtooth crash (the central chord data is shown in figure 8).
Several experiments on transient electron heat transport, such as modulated electron cyclotron heating, and impurity induced cold-pulse propagation have been carried in devices like ASDEX-U [41], ALCATOR-C [5], Frascati Tokamak Upgrade (FTU) [42], JT60 and Large Helical Device (LHD) [43]. The heat pulse propagation or the transient heat diffusivity, χ hp e in these heating-modulation experiments is observed to be much faster than the power balance estimations, χ pb e even in discharges which are in linear confinement regimes [LOC] [41]. The cold pulse propagation experiments in LOC regime also conclude the same [5]. It has also been shown that the fast core-heating (faster than the diffusion time-scales) is observed only in linear Ohmic confinement (LOC) discharges [44].
For the plasmas in LOC regime, fast propagation of transient heat pulse is explained via turbulent heat diffusivity due to presence of TEM [42]. The excitation of TEM depends on several parameters like, electron temperature gradient, collisionality, magnetic shear and density gradient [6]. Although, the sawtooth crash may be generating a local and sharp gradient different from the modulation experiments, and avalanche model of heat diffusivity may be a possibility, however, our experimental observations indicate otherwise as explained above. Furthermore, two sawtooth-crashes of equal magnitudes should generate similar local and sharp gradients and the heat pulse propagation in both the cases should remain same, which is in contrast to our experimental observations. As a sawtooth crash generates the local heat pulse at the q = 1 location, it seems to be quite similar to the heat pulse introduced by other means such as ECR heating etc. Hence, the heat pulse propagation velocity, in the absence of m/n = 2/1 and 3/1 MHD activity in the intermediate region, may be due to prevailing TEM turbulent transport in the LOC plasmas of ADITYA tokamak.
The discharges used in present study are in LOC regime, from the linear relation between plasma density and energy confinement time [45]. Also, the Gyro-kinetic simulation studies in similar LOC discharges [46] shows that TEM are most dominant modes in our machine [47]. In LOC regime, there is a possibility of existence of TEM turbulence and can contribute to electron heat diffusivity, given the electron temperature gradient in discharges is above the critical threshold [46]. The reasonable estimate of turbulent electron heat diffusivity can be made using empirical form derived from ECH power modulation study on ASDEX-U and TORE-SUPRA [1,41], where, χ TEM e is the transient electron heat diffusivity for TEM, λ is the constant factor, q is the safety factor, T e is the electron temperature, R is the major radius, R/L Te is the dimensionless electron temperature gradient, R/L cr Te is the critical threshold of electron temperature gradient for TEM and H is the Heaviside function. The analysed discharges are in LOC regime as established through many experimental and theoretical studies, it has been established that the TEM is the most dominant turbulent mode [46,48]. Therefore, by taking a reasonable critical threshold for TEM R/L cr Te ∼ 5, constant λ = 1 electron heat diffusivity at r = 15 cm estimated about χ TEM e ∼15 m 2 s −1 . This value still falls short by factor of four as compared to sawtooth induced transient heat pulse estimate. Thus, we see that, even if we include the contribution of TEM in the electron heat diffusivity, it does not completely explain fast propagation of sawtooth induced heat pulse. In short, along with turbulent transport, magnetic field topology, which is stochastic in nature, is likely contributing in the enhancement of electron heat diffusivity.
In fact, in TFTR [14], experimental and theoretical observation has shown that with sawtooth crash, the helical perturbation is observed to expand beyond mixing radius. This creates a region of stochastic magnetic field, and this stochastic magnetic field may be responsible for explaining the fast propagation of heat perturbation induced by sawtooth. However, the presence of island associated to MHD mode and its influence on fast propagation of sawtooth induced heat pulse has not been reported in any of the earlier studies [13][14][15][16][17][18][19]49]. Many experimental and theoretical investigations have reported the modification of plasma rotation, heat, particle and impurity transports, and current decay time during plasma disruption [38,50,[51][52][53][54] in the presence of MHD islands.
It is quite well-known that the magnetic field symmetry can be broken down by resonant magnetic field perturbations generated by MHD instabilities. Resonant magnetic perturbation coils are also known to be modify the magnetic field topology in tokamaks. With presence of two or more nearby magnetic islands and when they grow beyond a certain limit, they overlap and form a stochastic magnetic field region. In stochastic magnetic field, field lines are no longer constraint to a toroidal surface, but can wander stochastically [55,56]. This stochastic magnetic field region is observed to enhance electron heat diffusivity [57]. The free streaming orbit of particle parallel to the magnetic field line takes a radial excursion of the particles trajectory, leading to a radial energy diffusion resulting in fast propagation. Therefore, it is quite logical to investigate the role of stochastic magnetic field in creating necessary transport channel, which enhances the sawtooth induced heat pulse propagation from the plasma core to edge region. Thus, an attempt has been made to explain the experimentally estimated electron heat diffusivity and make a reasonable comparison with the estimation from the transport values in the presence of stochastic magnetic field.
Rechester and Rosenbluth [58] estimated the energy transport in the limit of strongly stochastic magnetic fields, quantified by large values of the stochasticity parameter or Chirikov overlap area. The formation of stochastic magnetic field due to overlapping of adjacent magnetic island structures, stochasticity or Chirikov parameter S for these island widths is calculated using the formula [55,56], where w m and w n are the width of the island and r m and r n are the resonance location of the magnetic islands associated with modes m and n, respectively. Using the estimated island widths during sawtooth crash in the ADITYA tokamak as shown in figure 6, the stochasticity parameter, S is found to be around 0.95-1.20, indicating the presence of stochastic magnetic field in the confinement region of plasma during sawtooth crash in ADITYA tokamak. The estimation of electron heat diffusivity in stochastic magnetic field can be made from relation [58,59], where v e,th is the electron thermal velocity, q is the safety factor, R is the major radius, B T is the toroidal magnetic field and δB r is the magnitude of radial magnetic field fluctuation.
With the typical plasma parameters, δB r /B T ∼ 3.5 × 10 −4 , r s ∼ 0.15 m, R = 0.75 m, B T ∼ 0.62 T, using equation (6), electron heat diffusivity χ S e comes about ∼20 − 25 m 2 s −1 at r = 15 cm near the location of m/n = 2/1 resonance surface. Here, the radial magnetic field component B r is calculated using the equation, B r ∼ = S a m+1 B p , where S is the distance from magnetic probe to the resonance surface and a is the minor radius of the device [60]. Moreover, recent studies have shown, that the propagation of heat pulse shows different characteristics depending on presence of magnetic island or stochastization of magnetic field [61]. Heat pulse time lag analysis is carried out for plasma discharges with relatively strong and weak MHD activity. The time-lag between the observed peaks in the successive ECE channel is plotted with the square of the minor radius in figure 7 for two discharges (shot #14139 with strong and shot #14176 with weak MHD activity). A clear difference in slope show the heat pulse propagation gets modified in the presence of stochastization of the magnetic field can be easily noticed. We find that difference in the slope of these two time-lag curves indicate that the heat pulse speed is observed to increase by 30%-40% due to magnetic field stochastization in ADITYA. Such a bifurcation in heat propagation characteristics is also reported in [61].
Furthermore, in figure 10, the total time lag (between SXR and edge channel of ECE at = 0.92) of heat pulse arrival at the edge is plotted against the magnitude of the B θ fluctuations corresponding to the MHD (m/n = 2/1 and 3/1) activity present in the intermediate region, a measure of island widths. The figure clearly shows that as the island grows bigger the heat-pulse propagation velocity increases almost proportionally with the increase in δB p /B p .
Thus, the diffusivity of the sawtooth-induced heat pulse observed in the MHD active ADITYA discharges seem to be a combined effect of heat propagation through magnetic field stochasticity generated by MHD island overlapping and through TEM turbulence. Contributions of these abovementioned effects when added to the power balance estimation gives χ hp e = χ pb e + χ TEM e + χ S e ≈ 45 − 50 m 2 s −1 , which qualitatively explains the measured heat diffusivities of 50-60 m 2 s −1 in ADITYA within the experimental errors. Where χ hp e , χ pb e , χ TEM e and χ S e is electron heat diffusivity due to, transient sawtooth induced heat pulse, power balance, TEM turbulence and stochastization of magnetic field lines respectively.

Conclusion
Fast propagation of sawtooth induced heat pulse is observed in the MHD active plasma of ADITYA tokamak. The sawtooth crash deposits heat beyond the inversion radius, which gets transported to the edge region of the plasma, and is reflected as inverted sawtooth modulation in the edge channels of ECE and H α spectral line emission. The inverse-sawtooth modulation in edge channels of ECE and H α signals are pronouncedly visible in the discharges which have significant MHD activity. The time-lag analysis on ECE signals from different radii reveal the propagation time from plasma core to edge of ∼150 µs. The transport of transient electron heat pulse is found to be diffusive in nature as the time-lag analysis of ECE signals from various radii follows a r 2 dependency. The measured time-lag corresponds to an effective electron heat diffusivity χ hp e (strong MHD) ≈ 50 − 60 m 2 s −1 in relatively strong MHD active plasma, which is approximately an order higher than those calculated from the power balance, χ hp e ∼ 10χ pb e . While, plasma discharge with relatively weak MHD activity, the effective electron heat diffusivity χ hp e (weak MHD) ≈ 35 − 40 m 2 s −1 . Therefore, the contribution due to MHD activity is nearly about 20 − 25 m 2 s −1 , which is in good agreement with the electron heat diffusivity calculated with magnetic perturbation. Detailed analysis reveals that the stochastization of magnetic field in the intermediate confinement region between, q = 1 surface and plasma edge of ADITYA, via overlapping of 2/1 and 3/1 drift tearing modes is one of prime contributors of the observed enhanced electron heat diffusivity. Thus, the electron heat diffusivity quantified by adding the contributions from the magnetic field stochastization and TEM turbulence to the gross power balance electron heat diffusivity, matches fairly well with the measured heat diffusivity following a sawtooth crash event in an ADITYA discharge. The electron heat diffusivity of the sawtooth-induced heat pulse observed in the MHD active ADITYA discharges seem to be a combined effect of heat propagation through magnetic field stochasticity generated by MHD island overlapping and through turbulence. Contributions of these abovementioned effects when added to the power balance estimation gives χ hp e = χ pb e + χ TEM e + χ S e ≈ 45 − 50 m 2 s −1 , which qualitatively explains the estimated effective heat diffusivities of 50-60 m 2 s −1 in ADITYA within the experimental errors. The heat pulse propagation speed is found to be in good agreement with the avalanche model estimates. However, observations of different heat pulse propagation speeds corresponding to equal magnitude sawtooth-crashes in the presence and absence of MHD (m/n = 2/1, 3/1) activity do not support the avalanche model.