The solar wind exhibits fluctuations over a broad range of timescales characteristic of magnetohy... more The solar wind exhibits fluctuations over a broad range of timescales characteristic of magnetohydrodynamic (MHD) turbulence evolving in the presence of structures of coronal origin. In- situ spacecraft observations of plasma parameters are at minute (or below) resolution for intervals spanning the solar cycle and provide a large number of samples for statistical studies. The magnetic field power spectrum typically has two characteristic components, an inertial range of turbulence over several orders of magnitude with approximately Kolmogorov power law and at lower frequencies, an approximately '1/f' energy containing range believed to be of direct coronal origin. We focus on the behaviour of in- situ observations of fluctuations in the inner heliosphere as a function of solar cycle and solar wind speed; that is, with respect to coronal structure and dynamics. We employ a recently developed technique that sensitively distinguishes between fractal and multifractal scaling in the timeseries. Our working hypothesis is that since the latter can be characteristic of local MHD turbulence, the former maps more directly to features of coronal origin. We find a strong correlation between the scaling properties of magnetic energy density fluctuations and the magnetic complexity of the coronal magnetic fields. At solar maximum in the ecliptic, where the in- situ observations can be dominated by slow solar wind, the magnetic energy density as seen by WIND and ACE shows a fractal signature, whereas at minimum it is multifractal. This is corroborated by ULLYSES polar observations at solar minimum in quiet, fast solar wind where again, multifractal scaling is found. This high magnetic complexity in the corona corresponds to fractal, rather than multifractal scaling in magnetic energy density; remarkably, this fractal signature dominates the full dynamic range of observations, extending across timescales typically identified with both the '1/f' and 'inertial range'. The correlation of behaviour of other bulk plasma parameters observed in- situ with the magnetic complexity of the coronal will also be discussed. Since we are able to quantify scaling exponents, our results provide constraints on models for the solar wind. In particular, the fractal signature which we discuss here can be captured by a nonlinear Fokker Planck model, with the prospect of a quantitative mapping back to the corona.
ABSTRACT Quantifying the spectrum of sizes and durations of large and/or long-lived fluctuations ... more ABSTRACT Quantifying the spectrum of sizes and durations of large and/or long-lived fluctuations in complex, multi-scale, space plasmas is a topic of both theoretical and practical importance. The predictions of inherently multi-scale physical theories such as MHD turbulence have given one direct stimulus for its investigation. There are also space weather implications to an improved ability to assess the likelihood of an extreme fluctuation of a given size. Our intuition as scientists tends to be formed on the familiar Gaussian "normal" distribution, which has a very low likelihood of extreme fluctuations. Perhaps surprisingly, there is both theoretical and observational evidence that favours non-Gaussian, heavier-tailed, probability distributions for some space physics datasets. Additionally there is evidence for the existence of long-ranged memory between the values of fluctuations. In this talk I will show how such properties can be captured in a preliminary way by a self-similar, fractal model. I will show how such a fractal model can be used to make predictions for experimental accessible quantities like the size and duration of a buurst (a sequence of values that exceed a given threshold), or the survival probability of a burst [c.f. preliminary results in Watkins et al, PRE, 2009]. In real-world time series scaling behaviour need not be "mild" enough to be captured by a single self-similarity exponent H, but might instead require a "wild" multifractal spectrum of scaling exponents [e.g. Rypdal and Rypdal, JGR, 2011; Moloney and Davidsen, JGR, 2011] to give a complete description. I will discuss preliminary work on extending the burst approach into the multifractal domain [see also Watkins et al, chapter in press for AGU Chapman Conference on Complexity and Extreme Events in the Geosciences, Hyderabad].
Solar wind turbulence is dominated by Alfv\'{e}nic fluctuations but the power spectral expon... more Solar wind turbulence is dominated by Alfv\'{e}nic fluctuations but the power spectral exponents somewhat surprisingly evolve toward the Kolmogorov value of -5/3, that of hydrodynamic turbulence. We show that at 1AU the turbulence decomposes linearly into two coexistent components perpendicular and parallel to the local average magnetic field. The first of these is consistent with propagating Alfv\'{e}n wavepackets and shows
An avalanche or ''sandpile'' model is discussed that generalizes the original self-organized crit... more An avalanche or ''sandpile'' model is discussed that generalizes the original self-organized criticality avalanche model of Bak, Tang, and Wiesenfeld ͓Phys. Rev. Lett. 59, 381 ͑1987͔͒ to include spatially extended local redistribution. A single control parameter specifies the spatial extent of local redistribution when the critical gradient is exceeded: this has profound consequences for nonlocal avalanching transport and for the dynamical behavior of the system, which are insensitive to other details such as the initial conditions and fluctuations in fueling or the critical gradient. The model possesses essentially two regimes of behavior. If the scale of nonlocal transport is of the order of the system size, the system is in the vicinity of a fixed point; in consequence the statistics of energy dissipation and length of avalanches are power law, and the time evolution is irregular ͑''intermittent''͒. If this scale is significantly smaller than the system size, the time evolution is quasiregular and follows a limit cycle. The first of these regimes appears relevant to the earth's magnetosphere, where bursty transport and large scale reconfiguration ͑substorms͒ are observed. In this case the avalanche statistics have been inferred from observations of patches of intensity in the aurora, which may map to energy dissipation events in the magnetotail. The second regime displays significant links to the observed confinement phenomenology of magnetic fusion plasmas, corresponding to a broader range of model parameter space. For example, there is correlation between sandpile profiles, stored energy, and edge steepening on the one hand, and the control parameter on the other.
ABSTRACT The effects of spatially varying magnetic field strength on the scaling properties of pl... more ABSTRACT The effects of spatially varying magnetic field strength on the scaling properties of plasma turbulence, modelled by an extended form of Hasegawa-Wakatani model, are investigated. We study changes in the intermittency of the velocity, density, and vorticity fields, as functions of the magnetic field inhomogeneity C = −∂ ln B/∂x. While the velocity fluctuations are always self-similar and their scaling is unaffected by the value of C, the intermittency levels in density and vorticity change with parameter C, reflecting morphological changes in the coherent structures due to the interchange mechanism. Given the centrality of vorticity in conditioning plasma transport, this result is of interest in scaling the results of transport measurements and simulations in tokamak edge plasmas, where drift-interchange turbulence in the presence of a magnetic field gradient is likely to occur.
The scrape-off layer (SOL) of fusion devices is typically composed of filamentary structures that... more The scrape-off layer (SOL) of fusion devices is typically composed of filamentary structures that propagate with a high radial velocity away from the bulk plasma. When radial and parallel transport times are comparable, these coherent structures constitute an intermittent heat and particle flux which can reach the material wall; in time causing wear to plasma facing components. Qualitative models predict that the parallel currents, driven by the divertor sheath, have a direct impact on this radial velocity. In this work, the predictions for radial velocity of plasma filaments in the SOL from models are tested against data from the MAST tokamak and simulation. We apply a statistical method of window averaging to MAST Langmuir probe data in order to examine the scaling of the radial velocity of filaments with the plasma density inside the filaments. Our analysis strongly suggests that the radial dynamics emerge from the competition of multiple mechanisms and not from a single process. At intermediate distances from the bulk plasma, a new model proposed here, in which the parallel current depends on a constant target density appears to be the most relevant for the MAST plasma. This is confirmed using a TOKAM2D simulation with a modified parallel current term.
The extended Hasegawa-Wakatani equations generate fully nonlinear self-consistent solutions for c... more The extended Hasegawa-Wakatani equations generate fully nonlinear self-consistent solutions for coupled density n and vorticity ٌ 2 , where is electrostatic potential, in a plasma with background density inhomogeneity ץ−= ln n 0 / ץx and magnetic field strength inhomogeneity C ץ−= ln B / ץx. Finite C introduces interchange effects and ٌB drifts into the framework of drift turbulence through compressibility of the E ϫ B and diamagnetic drifts. This paper addresses the direct computation of the radial E ϫ B density flux ⌫ n =−n ץ / ץy, tracer particle transport, the statistical properties of the turbulent fluctuations that drive ⌫ n and tracer motion, and analytical underpinnings. Systematic trends emerge in the dependence on C of the skewness of the distribution of pointwise ⌫ n and in the relative phase of density-velocity and density-potential pairings. It is shown how these effects, together with conservation of potential vorticity ⌸ = ٌ 2 − n + ͑ − C͒x, account for much of the transport phenomenology. Simple analytical arguments yield a Fickian relation ⌫ n = ͑ − C͒D x between the radial density flux ⌫ n and the radial tracer diffusivity D x , which is shown to explain key trends in the simulations.
The evolution of magnetospheric indices on temporal scales shorter than that of substorms is char... more The evolution of magnetospheric indices on temporal scales shorter than that of substorms is characterized by bursty, intermittent events that may arise from turbulence intrinsic to the magnetosphere or may reflect solar wind-magnetosphere coupling. This leads to a generic problem of distinguishing between the features of the system and those of the driver. We quantify scaling properties of short term (up to few hours) fluctuations in the geomagnetic indices AL and AU during solar minimum and maximum along with the parameter ǫ that is a measure of the solar wind driver. We find that self-similar statistics provide a good approximation for the observed scaling properties of fluctuations in the geomagnetic indices, regardless of the solar activity level, and in the ǫ parameter at solar maximum. This self-similarity persists for fluctuations on time scales at least up to about 1 − 2 hours. The scaling exponent of AU index fluctuations show dependence on the solar cycle and the trend follows that found in the scaling of fluctuations in ǫ. The values of their corresponding scaling exponents, however, are always distinct. Fluctuations in the AL index are insensitive to the solar cycle as well as being distinct from those in the ǫ parameter. This approximate self-similar scaling leads to a Fokker-Planck model which, we show, captures the probability density function of fluctuations and provides a stochastic dynamical equation (Langevin equation) for time series of the geomagnetic indices.
We address the generic problem of extracting the scaling exponents of a stationary, self-affine p... more We address the generic problem of extracting the scaling exponents of a stationary, self-affine process realised by a timeseries of finite length, where information about the process is not known a priori. Estimating the scaling exponents relies upon estimating the moments, or more typically structure functions, of the probability density of the differenced timeseries. If the probability density is heavy tailed, outliers strongly influence the scaling behaviour of the moments. From an operational point of view, we wish to recover the scaling exponents of the underlying process by excluding a minimal population of these outliers. We test these ideas on a synthetically generated symmetric α-stable Lévy process and show that the Lévy exponent is recovered in up to the 6 th order moment after only ∼0.1-0.5% of the data are excluded. The scaling properties of the excluded outliers can then be tested to provide additional information about the system.
Scaling and a departure from Gaussian statistics has been identified as a key property of magneto... more Scaling and a departure from Gaussian statistics has been identified as a key property of magnetospheric energy release in the form of bursty bulk flows in the magnetotail, ``blobs" in the aurora, non-Gaussian fluctuations in geomagnetic indices and in single station magnetometer data. Models include Self-Organized Criticality (SOC) and multi-fractal models related to those of turbulence. We study scaling in fluctuations of the AU and AL geomagnetic indices that provide a measure of magnetospheric activity, and of the epsilon parameter which is a measure of the solar wind driver. We perform analyses that provide quantitative measures within the framework of models for turbulence and for critical phenomena; that is, we find the exponent that captures the self-similarity in the time series, and the functional form of the non-Gaussian Probability Density Function (PDF) that expresses its intermittency. Generalized structure function analysis is accompanied by PDF rescaling. Fluctuations in all quantities are found to exhibit self-similar statistics for up to 1-2 hours for fluctuation size up to 10 standard deviations. We divide the data into intervals of solar maximum and minimum and find that whereas fluctuations in epsilon and AU change their properties with the solar cycle, fluctuations in AL do not. This places strong statistical constraints on the propagation of information from these below-substorm scale fluctuations from the solar wind to the magnetosphere as seen by the indices. Having established scaling in AU and AL we then develop a Fokker-Planck model for their timeseries which we test against the PDF of the fluctuation timeseries. This provides a Langevin (stochastic dynamical) equation for the fluctuations in the indices.
... Authors: Watkins, NW; Credgington, D.; Hnat, B.; Chapman, SC; Freeman, MP; Greenhough, J ... ... more ... Authors: Watkins, NW; Credgington, D.; Hnat, B.; Chapman, SC; Freeman, MP; Greenhough, J ... many aspects of the natural world In the time series context he proposed the use of fractional Brownian motion fBm to model non-negligible temporal persistence the Joseph Effect and ...
Bulletin of the American Physical Society, Oct 30, 2012
Zonal flows are important in fusion plasma where they regulate drift wave turbulence and improve ... more Zonal flows are important in fusion plasma where they regulate drift wave turbulence and improve plasma confinement. Two mechanisms can lead to the creation of zonal flows: an inverse cascade of energy, similar to that observed for 2D turbulence, and a coupling between wave modes known as the modulational instability. This work focused on the modulational instability; a four mode truncation of the extended Hasegawa-Mima system was derived to model this. The extended Hasegawa-Mima model is more appropriate for ...
A statistical relationship between magnetic reconnection, current sheets, and intermittent turbul... more A statistical relationship between magnetic reconnection, current sheets, and intermittent turbulence in the solar wind is reported for the first time using in situ measurements from the Wind spacecraft at 1 AU. We identify intermittency as non-Gaussian fluctuations in increments of the magnetic field vector B that are spatially and temporally nonuniform. The reconnection events and current sheets are found to be concentrated in intervals of intermittent turbulence, identified using the partial variance of increments method: within the most non-Gaussian 1% of fluctuations in B, we find 87%-92% of reconnection exhausts and ∼9% of current sheets. Also, the likelihood that an identified current sheet will also correspond to a reconnection exhaust increases dramatically as the least intermittent fluctuations are removed from the data set. Hence, the turbulent solar wind contains a hierarchy of intermittent magnetic field structures that are increasingly linked to current sheets, which in turn are progressively more likely to correspond to sites of magnetic reconnection. These results could have far reaching implications for laboratory and astrophysical plasmas where turbulence and magnetic reconnection are ubiquitous.
The solar wind exhibits fluctuations over a broad range of timescales characteristic of magnetohy... more The solar wind exhibits fluctuations over a broad range of timescales characteristic of magnetohydrodynamic (MHD) turbulence evolving in the presence of structures of coronal origin. In- situ spacecraft observations of plasma parameters are at minute (or below) resolution for intervals spanning the solar cycle and provide a large number of samples for statistical studies. The magnetic field power spectrum typically has two characteristic components, an inertial range of turbulence over several orders of magnitude with approximately Kolmogorov power law and at lower frequencies, an approximately '1/f' energy containing range believed to be of direct coronal origin. We focus on the behaviour of in- situ observations of fluctuations in the inner heliosphere as a function of solar cycle and solar wind speed; that is, with respect to coronal structure and dynamics. We employ a recently developed technique that sensitively distinguishes between fractal and multifractal scaling in the timeseries. Our working hypothesis is that since the latter can be characteristic of local MHD turbulence, the former maps more directly to features of coronal origin. We find a strong correlation between the scaling properties of magnetic energy density fluctuations and the magnetic complexity of the coronal magnetic fields. At solar maximum in the ecliptic, where the in- situ observations can be dominated by slow solar wind, the magnetic energy density as seen by WIND and ACE shows a fractal signature, whereas at minimum it is multifractal. This is corroborated by ULLYSES polar observations at solar minimum in quiet, fast solar wind where again, multifractal scaling is found. This high magnetic complexity in the corona corresponds to fractal, rather than multifractal scaling in magnetic energy density; remarkably, this fractal signature dominates the full dynamic range of observations, extending across timescales typically identified with both the '1/f' and 'inertial range'. The correlation of behaviour of other bulk plasma parameters observed in- situ with the magnetic complexity of the coronal will also be discussed. Since we are able to quantify scaling exponents, our results provide constraints on models for the solar wind. In particular, the fractal signature which we discuss here can be captured by a nonlinear Fokker Planck model, with the prospect of a quantitative mapping back to the corona.
ABSTRACT Quantifying the spectrum of sizes and durations of large and/or long-lived fluctuations ... more ABSTRACT Quantifying the spectrum of sizes and durations of large and/or long-lived fluctuations in complex, multi-scale, space plasmas is a topic of both theoretical and practical importance. The predictions of inherently multi-scale physical theories such as MHD turbulence have given one direct stimulus for its investigation. There are also space weather implications to an improved ability to assess the likelihood of an extreme fluctuation of a given size. Our intuition as scientists tends to be formed on the familiar Gaussian "normal" distribution, which has a very low likelihood of extreme fluctuations. Perhaps surprisingly, there is both theoretical and observational evidence that favours non-Gaussian, heavier-tailed, probability distributions for some space physics datasets. Additionally there is evidence for the existence of long-ranged memory between the values of fluctuations. In this talk I will show how such properties can be captured in a preliminary way by a self-similar, fractal model. I will show how such a fractal model can be used to make predictions for experimental accessible quantities like the size and duration of a buurst (a sequence of values that exceed a given threshold), or the survival probability of a burst [c.f. preliminary results in Watkins et al, PRE, 2009]. In real-world time series scaling behaviour need not be "mild" enough to be captured by a single self-similarity exponent H, but might instead require a "wild" multifractal spectrum of scaling exponents [e.g. Rypdal and Rypdal, JGR, 2011; Moloney and Davidsen, JGR, 2011] to give a complete description. I will discuss preliminary work on extending the burst approach into the multifractal domain [see also Watkins et al, chapter in press for AGU Chapman Conference on Complexity and Extreme Events in the Geosciences, Hyderabad].
Solar wind turbulence is dominated by Alfv\'{e}nic fluctuations but the power spectral expon... more Solar wind turbulence is dominated by Alfv\'{e}nic fluctuations but the power spectral exponents somewhat surprisingly evolve toward the Kolmogorov value of -5/3, that of hydrodynamic turbulence. We show that at 1AU the turbulence decomposes linearly into two coexistent components perpendicular and parallel to the local average magnetic field. The first of these is consistent with propagating Alfv\'{e}n wavepackets and shows
An avalanche or ''sandpile'' model is discussed that generalizes the original self-organized crit... more An avalanche or ''sandpile'' model is discussed that generalizes the original self-organized criticality avalanche model of Bak, Tang, and Wiesenfeld ͓Phys. Rev. Lett. 59, 381 ͑1987͔͒ to include spatially extended local redistribution. A single control parameter specifies the spatial extent of local redistribution when the critical gradient is exceeded: this has profound consequences for nonlocal avalanching transport and for the dynamical behavior of the system, which are insensitive to other details such as the initial conditions and fluctuations in fueling or the critical gradient. The model possesses essentially two regimes of behavior. If the scale of nonlocal transport is of the order of the system size, the system is in the vicinity of a fixed point; in consequence the statistics of energy dissipation and length of avalanches are power law, and the time evolution is irregular ͑''intermittent''͒. If this scale is significantly smaller than the system size, the time evolution is quasiregular and follows a limit cycle. The first of these regimes appears relevant to the earth's magnetosphere, where bursty transport and large scale reconfiguration ͑substorms͒ are observed. In this case the avalanche statistics have been inferred from observations of patches of intensity in the aurora, which may map to energy dissipation events in the magnetotail. The second regime displays significant links to the observed confinement phenomenology of magnetic fusion plasmas, corresponding to a broader range of model parameter space. For example, there is correlation between sandpile profiles, stored energy, and edge steepening on the one hand, and the control parameter on the other.
ABSTRACT The effects of spatially varying magnetic field strength on the scaling properties of pl... more ABSTRACT The effects of spatially varying magnetic field strength on the scaling properties of plasma turbulence, modelled by an extended form of Hasegawa-Wakatani model, are investigated. We study changes in the intermittency of the velocity, density, and vorticity fields, as functions of the magnetic field inhomogeneity C = −∂ ln B/∂x. While the velocity fluctuations are always self-similar and their scaling is unaffected by the value of C, the intermittency levels in density and vorticity change with parameter C, reflecting morphological changes in the coherent structures due to the interchange mechanism. Given the centrality of vorticity in conditioning plasma transport, this result is of interest in scaling the results of transport measurements and simulations in tokamak edge plasmas, where drift-interchange turbulence in the presence of a magnetic field gradient is likely to occur.
The scrape-off layer (SOL) of fusion devices is typically composed of filamentary structures that... more The scrape-off layer (SOL) of fusion devices is typically composed of filamentary structures that propagate with a high radial velocity away from the bulk plasma. When radial and parallel transport times are comparable, these coherent structures constitute an intermittent heat and particle flux which can reach the material wall; in time causing wear to plasma facing components. Qualitative models predict that the parallel currents, driven by the divertor sheath, have a direct impact on this radial velocity. In this work, the predictions for radial velocity of plasma filaments in the SOL from models are tested against data from the MAST tokamak and simulation. We apply a statistical method of window averaging to MAST Langmuir probe data in order to examine the scaling of the radial velocity of filaments with the plasma density inside the filaments. Our analysis strongly suggests that the radial dynamics emerge from the competition of multiple mechanisms and not from a single process. At intermediate distances from the bulk plasma, a new model proposed here, in which the parallel current depends on a constant target density appears to be the most relevant for the MAST plasma. This is confirmed using a TOKAM2D simulation with a modified parallel current term.
The extended Hasegawa-Wakatani equations generate fully nonlinear self-consistent solutions for c... more The extended Hasegawa-Wakatani equations generate fully nonlinear self-consistent solutions for coupled density n and vorticity ٌ 2 , where is electrostatic potential, in a plasma with background density inhomogeneity ץ−= ln n 0 / ץx and magnetic field strength inhomogeneity C ץ−= ln B / ץx. Finite C introduces interchange effects and ٌB drifts into the framework of drift turbulence through compressibility of the E ϫ B and diamagnetic drifts. This paper addresses the direct computation of the radial E ϫ B density flux ⌫ n =−n ץ / ץy, tracer particle transport, the statistical properties of the turbulent fluctuations that drive ⌫ n and tracer motion, and analytical underpinnings. Systematic trends emerge in the dependence on C of the skewness of the distribution of pointwise ⌫ n and in the relative phase of density-velocity and density-potential pairings. It is shown how these effects, together with conservation of potential vorticity ⌸ = ٌ 2 − n + ͑ − C͒x, account for much of the transport phenomenology. Simple analytical arguments yield a Fickian relation ⌫ n = ͑ − C͒D x between the radial density flux ⌫ n and the radial tracer diffusivity D x , which is shown to explain key trends in the simulations.
The evolution of magnetospheric indices on temporal scales shorter than that of substorms is char... more The evolution of magnetospheric indices on temporal scales shorter than that of substorms is characterized by bursty, intermittent events that may arise from turbulence intrinsic to the magnetosphere or may reflect solar wind-magnetosphere coupling. This leads to a generic problem of distinguishing between the features of the system and those of the driver. We quantify scaling properties of short term (up to few hours) fluctuations in the geomagnetic indices AL and AU during solar minimum and maximum along with the parameter ǫ that is a measure of the solar wind driver. We find that self-similar statistics provide a good approximation for the observed scaling properties of fluctuations in the geomagnetic indices, regardless of the solar activity level, and in the ǫ parameter at solar maximum. This self-similarity persists for fluctuations on time scales at least up to about 1 − 2 hours. The scaling exponent of AU index fluctuations show dependence on the solar cycle and the trend follows that found in the scaling of fluctuations in ǫ. The values of their corresponding scaling exponents, however, are always distinct. Fluctuations in the AL index are insensitive to the solar cycle as well as being distinct from those in the ǫ parameter. This approximate self-similar scaling leads to a Fokker-Planck model which, we show, captures the probability density function of fluctuations and provides a stochastic dynamical equation (Langevin equation) for time series of the geomagnetic indices.
We address the generic problem of extracting the scaling exponents of a stationary, self-affine p... more We address the generic problem of extracting the scaling exponents of a stationary, self-affine process realised by a timeseries of finite length, where information about the process is not known a priori. Estimating the scaling exponents relies upon estimating the moments, or more typically structure functions, of the probability density of the differenced timeseries. If the probability density is heavy tailed, outliers strongly influence the scaling behaviour of the moments. From an operational point of view, we wish to recover the scaling exponents of the underlying process by excluding a minimal population of these outliers. We test these ideas on a synthetically generated symmetric α-stable Lévy process and show that the Lévy exponent is recovered in up to the 6 th order moment after only ∼0.1-0.5% of the data are excluded. The scaling properties of the excluded outliers can then be tested to provide additional information about the system.
Scaling and a departure from Gaussian statistics has been identified as a key property of magneto... more Scaling and a departure from Gaussian statistics has been identified as a key property of magnetospheric energy release in the form of bursty bulk flows in the magnetotail, ``blobs" in the aurora, non-Gaussian fluctuations in geomagnetic indices and in single station magnetometer data. Models include Self-Organized Criticality (SOC) and multi-fractal models related to those of turbulence. We study scaling in fluctuations of the AU and AL geomagnetic indices that provide a measure of magnetospheric activity, and of the epsilon parameter which is a measure of the solar wind driver. We perform analyses that provide quantitative measures within the framework of models for turbulence and for critical phenomena; that is, we find the exponent that captures the self-similarity in the time series, and the functional form of the non-Gaussian Probability Density Function (PDF) that expresses its intermittency. Generalized structure function analysis is accompanied by PDF rescaling. Fluctuations in all quantities are found to exhibit self-similar statistics for up to 1-2 hours for fluctuation size up to 10 standard deviations. We divide the data into intervals of solar maximum and minimum and find that whereas fluctuations in epsilon and AU change their properties with the solar cycle, fluctuations in AL do not. This places strong statistical constraints on the propagation of information from these below-substorm scale fluctuations from the solar wind to the magnetosphere as seen by the indices. Having established scaling in AU and AL we then develop a Fokker-Planck model for their timeseries which we test against the PDF of the fluctuation timeseries. This provides a Langevin (stochastic dynamical) equation for the fluctuations in the indices.
... Authors: Watkins, NW; Credgington, D.; Hnat, B.; Chapman, SC; Freeman, MP; Greenhough, J ... ... more ... Authors: Watkins, NW; Credgington, D.; Hnat, B.; Chapman, SC; Freeman, MP; Greenhough, J ... many aspects of the natural world In the time series context he proposed the use of fractional Brownian motion fBm to model non-negligible temporal persistence the Joseph Effect and ...
Bulletin of the American Physical Society, Oct 30, 2012
Zonal flows are important in fusion plasma where they regulate drift wave turbulence and improve ... more Zonal flows are important in fusion plasma where they regulate drift wave turbulence and improve plasma confinement. Two mechanisms can lead to the creation of zonal flows: an inverse cascade of energy, similar to that observed for 2D turbulence, and a coupling between wave modes known as the modulational instability. This work focused on the modulational instability; a four mode truncation of the extended Hasegawa-Mima system was derived to model this. The extended Hasegawa-Mima model is more appropriate for ...
A statistical relationship between magnetic reconnection, current sheets, and intermittent turbul... more A statistical relationship between magnetic reconnection, current sheets, and intermittent turbulence in the solar wind is reported for the first time using in situ measurements from the Wind spacecraft at 1 AU. We identify intermittency as non-Gaussian fluctuations in increments of the magnetic field vector B that are spatially and temporally nonuniform. The reconnection events and current sheets are found to be concentrated in intervals of intermittent turbulence, identified using the partial variance of increments method: within the most non-Gaussian 1% of fluctuations in B, we find 87%-92% of reconnection exhausts and ∼9% of current sheets. Also, the likelihood that an identified current sheet will also correspond to a reconnection exhaust increases dramatically as the least intermittent fluctuations are removed from the data set. Hence, the turbulent solar wind contains a hierarchy of intermittent magnetic field structures that are increasingly linked to current sheets, which in turn are progressively more likely to correspond to sites of magnetic reconnection. These results could have far reaching implications for laboratory and astrophysical plasmas where turbulence and magnetic reconnection are ubiquitous.
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Papers by B. Hnat