Observations of Transition from Imbalanced to Balanced Kinetic Alfvénic Turbulence

TL;DR

This study uses Parker Solar Probe measurements to diagnose kinetic Alfvénic turbulence in the near-Sun solar wind via a magnetic helicity framework. By constructing field-aligned coordinate systems and three complementary helicity methods, the authors identify KAWs and quantify the propagation-direction imbalance across ion and sub-ion scales. They observe a pronounced transition from imbalanced to balanced turbulence near ion scales, with the imbalance peaking around $f\sim5$ Hz (corresponding to $\rho_p k_\perp\sim1$) and then relaxing at smaller scales, supporting helicity-barrier predictions. The results reveal a nuanced picture of energy cascades, with implications for nonlocal transfer, damping, and the role of switchbacks, and call for refined kinetic-scale turbulence theories. Overall, the work provides a robust, multi-method framework for linking magnetic helicity measurements to wave modes and turbulence evolution in heliospheric plasmas.

Abstract

We report observations of solar wind turbulence derived from measurements by the Parker Solar Probe. Our findings reveal the emergence of finite magnetic helicity within the transition range of the turbulence, aligning with signatures of kinetic Alfvén waves (KAWs). Notably, as the wave scale transitions from super-ion to sub-ion scales, the ratio of KAWs with opposing signs of magnetic helicity initially increases from approximately 1 to 6.5 before returning to 1. This observation provides, for the first time, compelling evidence for the transition from imbalanced kinetic Alfvénic turbulence to balanced kinetic Alfvénic turbulence.

Figures (14)

• Figure 1: Plasma environment and magnetic helicity during the time interval from 09:30 UTC on 2018 November 04 to 21:20 UTC on 2018 November 07. (a) The magnitude and three components of the magnetic field ${\boldsymbol B}$ in the spacecraft frame. (b) The solar wind speed ${\boldsymbol V}$ in the spacecraft frame. (c) The distribution of $\sigma_\mathrm{m\perp_1\perp_2}$. (d) The distribution of $\sigma_\mathrm{m\perp_2 \parallel}$. (e) The distribution of $\sigma_\mathrm{m \parallel \perp_1}$. (f) The distribution of $\theta_\mathrm{VB}$. The gray curves in (c)--(e) denote the proton cyclotron frequency $f_{\mathrm{cp}}$. Because the merged magnetic field data in (a) contain gaps, no corresponding magnetic helicity or $\theta_{\mathrm{VB}}$ distributions are available in (c)–(f).
• Figure 2: (a) The $\sigma_{\mathrm{m\perp_2\parallel}}$ distribution in the $\theta_{\mathrm{VB}}$--$f$ space, where the gray curve denotes the Doppler shift frequency of quasi-perpendicular waves with $\rho_pk=1$. (b) The $\sigma_{\mathrm{m\perp_1\perp_2}}$ distribution in the $\theta_{\mathrm{VB}}$--$f$ space, where the black curve denotes the Doppler shift frequency of quasi-parallel waves with $\lambda_pk=0.6$ and $\theta=170^\circ$. (c) The power spectral density of the magnetic field $P_B$ in four different $\theta_{\mathrm{VB}}$ ranges: $75^\circ$--$90^\circ$, $90^\circ$--$105^\circ$, $105^\circ$--$120^\circ$, and $120^\circ$--$135^\circ$. (d) The $P_B$ as a function of the normalized wavenumber $Lk^*$, with $L=\rho_p$ (thick curve) and $L=\lambda_p$ (thin curve). In (c) and (d), the upper panels show $P_B$ with $\sigma_{\mathrm{m\perp_2\parallel}}$ overlaid, whereas the lower panels display the corresponding spectral indices $\alpha$.
• Figure 3: (a) The number of the data $N(\sigma_{\mathrm{m\perp_2\parallel}},f)$ normalized by the maximum $N(\sigma_{\mathrm{m\perp_2\parallel}},f)$ at each $f$, denoted by ${\bar{N}}(\sigma_{\mathrm{m\perp_2\parallel}},f)$. (b) The probability distribution function of $N(\sigma_{\mathrm{m\perp_2\parallel}},f)$, denoted by $\mathrm{PDF}$($\sigma_{\mathrm{m\perp_2\parallel}}$,$f$), at four typical frequencies: $f=$ 0.3, 3.1, 10.5, and 50.1 Hz. (c) The ratio $R(f)$ between the total data numbers with negative and positive $\sigma_{\mathrm{m\perp_2\parallel}}$, $R(f) = N_t(f,\sigma_{\mathrm{m\perp_2\parallel}} < 0)/N_t(f,\sigma_{\mathrm{m\perp_2\parallel}} > 0)$. (d) The ratio $R$ between the data numbers with negative and positive $\sigma_{\mathrm{m\perp_2\parallel}}$ in $k_\perp$--$k_\parallel$ space, where the grey curves are the contour lines of $P_B$. The data in (a)--(c) are limited to $|\theta_\mathrm{VB}-90^\circ|<45^\circ$, and the data in (d) are limited to $|\sigma_{\mathrm{m\perp_2\parallel}}/\sigma_{\mathrm{m\parallel\perp_1}}|>2$; all data are subject to the condition $|W_{\parallel}|^2/\left(|W_{\perp_1}|^2+|W_{\perp_2}|^2\right)<1$.
• Figure 4: (a) The field-aligned coordinate (FAC) system defined by the background magnetic field ${\boldsymbol B_0}$ and solar wind velocity ${\boldsymbol V_0}$, where $\hat{\boldsymbol e}_{\parallel} \equiv {\boldsymbol B_0} / {|{\boldsymbol B_0}|}$, $\hat{\boldsymbol e}_{\perp_1^{'}} \equiv \hat{\boldsymbol e}_{\perp_2^{'}} \times \hat{\boldsymbol e}_{\parallel}$, and $\hat{\boldsymbol e}_{\perp_2^{'}} \equiv {\boldsymbol B_0}\times{\boldsymbol V_0}/(|{\boldsymbol B_0}||{\boldsymbol V_0}|)$. (b) The rotation from $(\hat{\boldsymbol e}_{\perp_1^{'}}, \hat{\boldsymbol e}_{\perp_2^{'}})$ into $(\hat{\boldsymbol e}_{\perp_1}, \hat{\boldsymbol e}_{\perp_2})$, where $\phi$ represents the rotation angle between the two sets of coordinates.
• Figure 5: Overview of the reduced magnetic helicity distributions obtained from the two FAC methods. Top panel: The magnitude and the three components of the magnetic field in the spacecraft frame. Second to fourth panels: Distributions of $\sigma_\mathrm{m\perp^{'}_1 \perp^{'}_2}$, $\sigma_\mathrm{m\perp_2^{'} \parallel}$, and $\sigma_\mathrm{m\parallel \perp_1^{'}}$ from Method II. Fifth to seventh panels: Distributions of $\sigma_\mathrm{m\perp_1 \perp_2}$, $\sigma_\mathrm{m\perp_2 \parallel}$, and $\sigma_\mathrm{m\parallel \perp_1}$ from Method III.