This means that a part of the spectra belongs to intervals in the weak foreshock, downstream of IP shocks or within ICMEs. Number 2 This conclusion was based on an analysis of magnetic field variations. Its publishing company, IOP Publishing, is a world leader in professional scientific communications. Since the velocity break frequency is between the two breaks of the density spectrum, we can conclude that the breakdown of the MHD cascade happens in all fields in roughly the same place. The automated routine fits each individual smoothed spectrum with two power-law functions and the break point is determined as the frequency corresponding to their intersection. The Spearman rank correlation coefficients are given in the top part of each panel. (2015) and many other authors. Magnetic spectra are variable and ion instabilities occur as a function of the local plasma parameters. Figure 2 shows the latest results, taken from reference [ 8 ]. 2011, 2013a). The black line in panel (a) shows intermediate events. 2009). (2014a) argued that the break occurs at the gyrostructure frequency in high-β plasma but at the ion inertial length in the low-β environment. In situ solar wind measurements near ion scales have been rare up to now, and thus the purpose of this investigation is to estimate the power-law exponents and ion break frequency of the bulk and thermal velocity fluctuations at kinetic scales. 2011b; Chen et al. 2013), the spectra exhibit a break, and the density fluctuation spectrum exhibits a local flattening. The Astrophysical Journal, 1983; Muller & Grappin 2005; Boldyrev & Perez 2009, 2012; Chen et al. 2011) can be applied. However, computations of the speed and temperature are based on the derivative of the Faraday cup deceleration characteristics and this process increases the noise in the processed data. This approach reflects the properties of compressive as well as Alfvénic fluctuations. 2013a). The red lines display linear fits, and the values of their slopes are given within the panels. In order to reveal the unsteady features of gas–solid flow, the pressure fluctuations were measured at different locations along the length of the pipeline while conveying powders through the pipeline. Šafránková et al. The magnetic field exhibits an average spectral index close to −5/3 (e.g., Podesta & Borovsky 2010; Boldyrev et al. Power spectral density (PSD) functions were obtained for the analysis of the pressure fluctuation. The smoothed values are shown by the black rectangles. The velocity break frequency is always lower than both the inertial length frequency and the gyrostructure frequency. This panel is given for comparison and uses only 100 subintervals for smoothing. This slope is around −1.5 (between −1 and −2) in a great majority of the cases but even rare events with slopes in the range from −1 to 0 exhibit the same trend (Figure 3(b)). 2011). (2015). Luttrell & Richter studied power spectra of magnetic field and density fluctuations in the frequency range of 10 −4 −10 −2 Hz. Nevertheless, the correlation coefficients exceed 0.7 in all panels. Brownian motion is the integral of white noise, and integration of a signal increases the exponent \alpha by 2 whereas the inverse operation of differentiation decreases it by 2. The multipole power spectrum described in the preceding paragraphs and displayed in the figure below is derived from mathematical expansion of the CMB temperature fluctuations in terms of the functions mathematicians call spherical harmonics. (2013a). The concept and use of the power spectrum of a signal is fundamental in electrical engineering, especially in electronic communication systems, including radio communications, radars, and related systems, plus passive remote sensing technology. Dependence of slope 2 on (a) bulk and (b) thermal PSD spectra as a function of ion β. Note that 160 individual spectra overlap in the figure and the corresponding PSDs are shown by the small black dots. 2001; Salem et al. The spectral behavior of magnetic field or velocity fluctuations is usually analyzed using the sum of the power spectral densities of all three components. of nonlinearity when the first objects collapse in the Universe is then complete-ly determined, characterized by a power spectrum for density fluctuations, P (k). © 2016. In the next step, the PSD of fluid is converted to PSD of thermal stress by the frequency transfer function. Citation J. Šafránková et al 2016 ApJ 825 121, 1 Charles University, Faculty of Mathematics and Physics, V Holešovičkách 2, 180 00 Prague 8, Czech Republic, 2 Department of Physics, Imperial College London, London SW7 2AZ, UK, 3 Space Research Institute of Russian Academy of Sciences, Moscow, Russia, Profsoyuznaya ul. (2013a) found that both speeds exhibit a steeper spectrum with mean slopes of about −3.4 and that the deviation between the density and speed spectral indices results in different ion break frequencies. (2006, 2007) for the bulk velocity. Recently, a power-law spectrum of magnetic and density fluctuations with a spectral index close to −2.8 seems to have been established (e.g., Chen et al. (2009), the plateau in the density spectrum is caused by a dominance of kinetic Alfvén over MHD turbulence and, consequently, break point 2 is a characteristic of kinetic fluctuations rather than an indication of dissipation. It is then possible to infer the matter density fluctuations in the linear or quasi-linear regime, but one needs to recover the matter power spectrum from the spectrum of the transmitted flux, a task that requires the use of hydro-dynamical simulations for the corresponding cosmological model. (2015) using a two-step procedure: (1) A set of overlapped 20 minute basic subintervals is created and the FFT is computed at each subinterval. Select your desired journals and corridors below. Click here to close this overlay, or press the "Escape" key on your keyboard. FFT spectra computed on short time intervals (20 minutes are equal to about 4 × 104 data points) are often noisy and different techniques can be used to smooth them. Surprisingly, the largest correlation coefficient between fb and fL was found for a group of high-β events. As noted, magnetic field measurements are not available on board Spektr-R, and thus we use the propagated Wind magnetic field observations as a proxy. They investigated the nature of MHD fluctuations occurring both upstream and downstream of parallel sub- and supercritical fast forward IP shocks. Note that this comment is valid to all correlations given in the present paper. Blue points: the slope of the power-law function is assumed −3.1 and −4 for the innermost annulus 0–1.5 and for other six regions, respectively. 2011b; Chen et al. Figure 7 suggests that a scaling of the bulk speed variations obeys similar rules as the scaling of magnetic field turbulence analyzed in Chen et al. Figure 2. (1998) analyzed conditions for a cyclotron wave damping and suggested that kd = ω /vA + vth is the minimum wavenumber at which the resonant dissipation would be important. On the other hand, an analysis of the density variations (Figure 1(c)) revealed three power-law segments of the density spectrum, consistent with the study of Šafránková et al. This fact demonstrates the dependence of the spectral slopes of the bulk and thermal speeds on ion β, which is shown in Figure 9. Within this formalism, one usually considers the fractional energy density of the fluctuations, given by: Moreover, there are no simple, … This conclusion was supported with an analysis of magnetic field spectra and we have shown that it can be applied to the speed spectra as well. It is true for the extreme values of β analyzed there and probably for intermediate values as well. (2014a). The velocity power spectrum is consistent with cascade of turbulence and its slope is in a broad agreement with the slope for canonical Kolmogorov turbulence. A good correspondence of the bulk and thermal speed spectra is shown in Figure 3. The focus here will be on the spectral features of the resulting heat fluctuations. Export citation and abstract 2011a; Chen et al. Therefore, 1/f noise can not be obtained by the simple procedure of integration or of differentiation of such convenient signals. The panels of this figure show the parameters describing the shape of the thermal speed spectra (break point, Slope 1, and Slope 2) as a function of the same parameter of the bulk speed spectrum. However, both dependences are weak because, whereas a range of β is as broad as four orders of magnitude, the fb/fL ratio changes by a factor of about seven, and the fb/fg ratio by a factor of 20. A linear dependence of the density break point on this frequency suggests that the character of turbulence changes when the fluctuations become comparable to the proton gyroradius. Chen et al. The diagonal black lines indicate an equality of the given quantities. We analyze the fluctuations of an electronic thermal current across an idealized molecular junction. (2014a) suggested that the break point would be determined by the larger of two characteristic lengths; thus Figure 6(c) compares results of our analysis with this suggestion. Electronic instruments called spectrum analyzers are used to observe and measure the power spectra of signals. To test whether or not it can be used for speed fluctuations, we divided our set into three groups according to the ion β calculated from mean values of the magnetic field, proton temperature, and density on 20 minute intervals. Parameters of the frequency spectra of these quantities are compared with the analogous parameters of proton density spectra studied in Šafránková et al. (1991) reported that the velocity spectra are systematically less steep than the magnetic field spectra. This panel compares the slopes corresponding to the kinetic range and one can see that the steeper slope of the bulk speed spectrum shown in Figure 2 is a typical feature found for the majority of the analyzed intervals. Figure 2 presents medians of all frequency spectra of bulk and thermal speeds in our data set. Similar to many previous studies, we have found that the PSD of speeds can be well approximated with two power-law segments divided by a clear break (Figures 1(a) and (b)). It has a worldwide membership of around 50 000 comprising physicists from all sectors, as well as those with an interest in physics. the fluctuations prior to the onset. 2006, 2007; Podesta & Borovsky 2010; Boldyrev et al. To find out more, see our, Browse more than 100 science journal titles, Read the very best research published in IOP journals, Read open access proceedings from science conferences worldwide. 2012; Bruno & Carbone 2013; Howes 2015; Riazantseva et al. The resulting expression reproduces the result from linear perturbation theory for small values of the cosmic scale factor a. You will only need to do this once. The density fluctuations are often described by the power spectrum, here given by the dimensionless version Δ 2 (k) such that σ 2 = ∫ Δ 2 (k) d ln k , where k is the wavenumber in an isotropic universe so that it does not depend on direction (the wavelength of the Fourier components is 2π/k), and σ is the standard deviation of the density relative to the mean density. It works to advance physics research, application and education; and engages with policy makers and the public to develop awareness and understanding of physics. Each particular spectrum is shown by a small black dot, the red heavy lines stand for the medians computed in the range of a particular parameter and the second and third quartiles are denoted by the red dashed lines. 2008, 2009; Sahraoui et al. These variations can influence turbulence at shorter scales, which is the main subject of the present study. 2012; Kiyani et al. Figure 1. http://aurora.troja.mff.cuni.cz/spektr-r/project/. (2015), namely, it consists of three power-law segments that are divided by two break points. There are two possible interpretations of the spectral steepening: (1) the slope increases due to a predominance of the forcing from large scales over dissipation (Šafránková et al. This coefficient is equal to 1 if the two variables are monotonically related. The inertial length frequency, fL, is defined as the ratio fL = Vsw/ 2π L where L is the inertial length. For full access to this pdf, sign in to an existing account, or purchase an annual subscription. The slopes in the MHD range are around −1.4, i.e., close to the value of −1.5 suggested by Podesta et al. We evaluate the power spectrum for standard hot dark matter (HDM) and cold dark matter (CDM) spectra; in the latter case, we employ the truncated Zel'dovich approximation which has been shown previously to yield much better agreement with the results from N-body simulations in cases where the primordial power spectrum contains large amounts of power on small scales. (2014a), but this suggestion was based on a discussion of events with β > 10 and/or β < 0.03. (A A S ) journals as soon as they are published. Published 2016 July 11, https://doi.org/10.3847/0004-637X/825/2/121. The density spectrum exhibits all features described by Chen et al. 2015). The authors thank the Wind team for the magnetic field data. Since the density break-point frequency changes by an order of magnitude but the solar wind speed only cahnges by a factor of two, the spatial dimensions of turbulent eddies are more important. do not currently use the corridors. All selected time series were then broken into 20 minute subintervals, FFTs were computed, and the spectra were fitted with two power-law functions. The scaling of the speed break point with the gyrostructure frequency is shown in Figure 6(a) for low (blue) and high (red) groups of β. The difference between magnetic and kinetic energies is usually called residual energy. At the MHD scale, the slope of −1.45 for the speed spectrum was consistent with the finding of other authors (Podesta et al. The low-frequency limit (0.001 Hz) is determined by the length of the analyzed intervals, which was set to 20 minutes. 2015 for a discussion of different methods of smoothing). We cannot directly check this hypothesis due to the lack of magnetic field measurements on board Spektr-R. Šafránková et al. Figure 6. The largest correlation coefficient is for the break point between scales (Figure 3(a)) and we can conclude that these breaks are controlled by the same mechanism. The difference between power indices of bulk and thermal speeds is about 0.5 and it holds nearly in the whole range of observed slopes. Find out more. This duration was chosen as a compromise between the noise in the frequency spectrum that increases with decreasing interval length and variations of the background parameters. Since it is generally believed that ion β is an important factor influencing the compressibility of the system and thus the nature of the investigated fluctuations (Servidio et al. We show how, based on considerations on the observed form of the galaxy 2-point spatial correlation function xi(r), a very simplified -- yet surprisingly effective -- model for the linear density fluctuations power spectrum can be constructed. A comparison of corresponding panels in both Figures 7 and 8 reveals the following. Since the smoothing described above uses 1000 values, the rectangles merge in one black thick line and the individual points can be distinguished only at the frequencies above 1 Hz or in the density panel (panel (c)). Nevertheless, we will return to this point in the discussion. Since inertial length frequency is typically smaller than gyrostructure frequency for small β, the blue points and lines (low-β events) are nearly the same as the symbols in Figure 6(b). The only systematic difference between bulk and thermal speed velocity spectra is shown in Figure 3(c). Figure 7. According to Chandran et al. The density and speed break frequencies are both about equal to the gyrostructure frequency. The solar wind plasma is a strongly turbulent environment with electromagnetic fields and plasma properties that fluctuate over a wide range of timescales. The study is focused on the spectral properties around the break between MHD and ion kinetic scales and Šafránková et al. (2013b) and Šafránková et al. Power Spectral Density (PSD) is a frequency-domain plot of power per Hz vs frequency. 2006; Alexandrova et al. Since we expect a power-law spectrum, we do not use the mean values or medians but we fit all points falling into a given frequency interval with a straight line and apply the value of the fit in the middle of a particular interval as a smoothed value. Oxford University Press is a department of the University of Oxford. This work was supported in part by the project LH15136 financed by the Ministry of Education of the Czech Republic, and in part by the Czech Science Foundation under Contract 16-04956S. The dependences of these ratios on β are very clear, the correlation coefficients given at the top of the panels are high (0.7 and 0.3 for fb/fg and fb/fL, respectively). Figure 4. The frequency of the break point of the bulk (thermal) speed spectrum is at a lower frequency than break point 2 of the density spectrum, consistent with the preliminary study of Šafránková et al. 2011). (2) The whole frequency interval (0.001–2 Hz) is divided into 1000 equidistant parts on a logarithmic scale. The smoothed spectra of speeds are then fitted with two (the density spectrum in the panel 1(c) with three) straight lines and these fits are shown with red lines. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): We show how, based on considerations on the observed form of the galaxy two–point spatial correlation function ξ(r), a very simplified – yet surprisingly effective – model for the linear density fluctuations power spectrum can be constructed. On the other hand, Figure 7(c) shows that the scaling suggested by Leamon et al. The spectral indices at this range vary from −5 to −2 and differ by ≈0.5 with an exception of very flat spectra (Slope 2 of VSW > −2.5 in Figure 3(c)). The spectra were computed on short intervals and they are rather noisy, which results in a spread of their parameters. The slope −4 is obtained from the power spectrum of density fluctuations in the broad annulus 1.5–10.5 arcmin. © 2016. The power spectral density of the oscillator is composed of a term related to the high-frequency fluctuations in the feedback loop and a term related to the low-frequency fluctuations of the frequency control voltage. 1998; Smith et al. This frequency has a good physical meaning because the spacecraft in the solar wind would observe such a frequency if the structures of size RT are convected past. 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