Parker Solar Probe Orbit 24 Overview

• Parker Solar Probe Orbit 24 is a critical trajectory that enables deep in situ sampling (down to 9.8 R☉) to study solar wind acceleration, heating, and turbulence.
• Advanced MHD-turbulence models predict steep gradients in plasma, magnetic field, and temperature, highlighting major transitions from the outer wind to the perihelion zone.
• The observed variations in turbulence scales and the diminishing validity of the Taylor hypothesis demand modified analysis techniques for accurate near-Sun solar wind characterization.

The 24th orbit of the Parker Solar Probe (PSP) constitutes the mission’s deepest solar encounter, enabling in situ sampling within $r_{\text{min}}\approx9.8\,R_\odot$ of the Sun. This trajectory, achieved near the end of the seven-year mission, allows unprecedented examination of solar wind acceleration, heating, and turbulent properties close to the coronal base. Predictions for plasma and turbulence parameters along this orbit are based on global MHD models with self-consistent turbulence transport and heating, as well as empirical extrapolations constrained by remote-sensing and earlier in situ measurements (Chhiber et al., 2019, Venzmer et al., 2017).

1. Orbital Geometry and Kinematics

The geometry of orbit 24 is characterized by a semi-major axis $a\simeq0.473$ AU and an eccentricity $e\simeq0.906$, resulting in the radial distance:

$r(\theta) = \frac{a(1-e^2)}{1 + e\cos\theta},$

where $\theta$ is the true anomaly with perihelion at $\theta=0$ and $r_{\text{min}}=9.8\,R_\odot$. The trajectory samples heliocentric distances ranging from $r_{\text{min}}$ to $r_{\text{max}}=214\,R_\odot$ (near 0.99 AU) over a full orbit period of $\sim$120 days. The time between inbound $30\,R_\odot$ and perihelion is $\sim$3 days, facilitating detailed “fly-through” simulation of plasma parameters.

$\theta$ (deg)	$r$ ($R_\odot$)	Key point
–180	214	Aphelion
–60	30	Inbound outer
–30	20	Inbound mid
0	9.8	Perihelion
+30	20	Outbound mid
+60	30	Outbound outer
+180	214	Back to aphelion

2. Plasma and Turbulence Parameter Predictions

Simulations employing the Usmanov et al. (2018) two-scale MHD+turbulence model provide radial profiles for key plasma quantities. The PSP traverses regimes with steep spatial gradients and varying turbulence cross helicity.

$r$ ($R_\odot$)	$V$ (km/s)	$B$ (nT)	$n_p$ (cm$^{-3}$)	$T$ ($10^5$ K)	$Z^2$ ($10^3$ km$^2$/s$^2$)	$\lambda$ ($10^5$ km)	$\sigma_c$	$R$
30	260	40	150	0.20	3.0	1.0	0.90	$4.7\times10^6$
20	240	80	400	0.30	5.5	0.6	0.85	$1.9\times10^6$
9.8	180	180	1800	0.80	12.0	0.2	0.65	$3.2\times10^5$

• $Z^2\equiv\langle v'^2 + b'^2\rangle$, fluctuation energy per unit mass
• $\lambda$, correlation scale
• $\sigma_c\equiv2\langle v'\cdot b'\rangle/Z^2$, normalized cross helicity
• $R\equiv V_\mathrm{sw}\lambda/Z$, Taylor-hypothesis parameter

Empirical models fitted to OMNI/Helios data (Venzmer et al., 2017) predict for perihelion $r=0.046$ AU ($\approx9.8\,R_\odot$) in late 2024: $B_\mathrm{med}=943$ nT, $v_\mathrm{med}=290$ km/s, $n_\mathrm{med}=2950$ cm$^{-3}$, $T_\mathrm{med}=1.93\times10^6$ K.

3. Governing Turbulence Transport Equations

The turbulent transport is described by the following set of steady-state equations (time derivatives neglected), defining the evolution of key second-order statistics:

• Fluctuation energy:

$$(\mathbf{v}\cdot\nabla)Z^2 + Z^2(1-\sigma_D)\cdot\frac{1}{2}\nabla\cdot\mathbf{u} - (\mathbf{V}_A\cdot\nabla)(Z^2\sigma_c) \simeq -\alpha f^+(\sigma_c)\frac{Z^3}{\lambda}$$

• Cross helicity:

$$(\mathbf{v}\cdot\nabla)(Z^2\sigma_c) - (\mathbf{V}_A\cdot\nabla)Z^2 \simeq -\alpha f^-(\sigma_c)\frac{Z^3}{\lambda}$$

• Correlation scale:

$$(\mathbf{v}\cdot\nabla)\lambda = \beta f^+(\sigma_c)Z$$

where $f^+(\sigma_c)$ and $f^-(\sigma_c)$ are nonlinear functions of cross helicity; $\alpha$ and $\beta$ are Kármán–Taylor constants; $\sigma_D\approx-1/3$.

The turbulent heating rate per unit mass is

$Q_T = \frac{\alpha f^+(\sigma_c)Z^3}{2\lambda}.$

4. Implications for the Taylor “Frozen-in” Hypothesis

A central assumption for converting spacecraft time series to spatial spectra is the Taylor hypothesis, evaluated via

$R(r)=\frac{V_\mathrm{sw}\lambda}{Z}.$

A regime with $R\gg1$ indicates validity of the “frozen-in” approximation. While $R$ remains $\gg1$ for all $r$ on Orbit 24, it decreases by an order of magnitude at perihelion (from $R\sim 5\times10^6$ at $30\,R_\odot$ to $R\sim 3\times10^5$ at $9.8\,R_\odot$).

Near $r\sim10\,R_\odot$, the Alfvén speed $V_A$ approaches $V_\mathrm{sw}$ and the ratio $\delta V/V_\mathrm{sw}\sim0.2$, indicating that timescales associated with Alfvénic and nonlinear processes can no longer be neglected. Simulations show that wave propagation, rapid cross-field sampling, and large Elsässer amplitudes violate the standard Taylor hypothesis, so simple time-space conversions become unreliable at these heliocentric distances. Modified frozen-in assumptions (such as 2D convective sweeping or Alfvén-slab corrections) are only marginally valid inside $20\,R_\odot$ (Chhiber et al., 2019).

5. Radial Evolution and Physical Interpretation

As PSP approaches perihelion:

• Bulk flow: Decelerates from $260$ km/s ($30\,R_\odot$) to $180$ km/s at $9.8\,R_\odot$, then re-accelerates.
• Magnetic field: Increases as $B\propto r^{-1.8}$ from $40$ nT ($30\,R_\odot$) to $180$ nT at $9.8\,R_\odot$.
• Proton density: Scales as $n_p\propto r^{-2.2}$; from $150$ cm$^{-3}$ to $1800$ cm$^{-3}$.
• Temperature: Rises from $0.2\times10^5$ K to $0.8\times10^5$ K, indicating local plasma heating on approach.
• Turbulence energy $Z^2$: Increases by a factor $\sim4$ toward perihelion, consistent with less-processed, “younger” fluctuations.
• Correlation scale $\lambda$: Decreases by $\sim5\times$, reflecting shorter turbulent cascade times.
• Cross helicity $\sigma_c$: Declines from $\sim0.9$ (outer wind) to $\sim0.65$ near perihelion, indicating increased admixture of inward-propagating modes, particularly near the closed-field streamer belt.

6. Significance for In-situ Solar Wind Physics

PSP’s Orbit 24 probes the critical region inside the Alfvén radius ($r\sim10$–$20\,R_\odot$), where the solar wind velocity has not reached its asymptotic value and the temperature profile is dominated by coronal heating mechanisms rather than expansion. The interplay between theoretical predictions and in situ measurements will directly constrain acceleration and heating processes, the partition of energy among solar wind constituents, and the structure of turbulence.

The shift of turbulent spectra to higher frequencies in the spacecraft frame, due to increased $Z^2$ and reduced $\lambda$, complicates inertial-range comparisons with Earth-based observations. The observed $\delta B/B$ approaches $0.3$ at perihelion, suggesting dominant two-dimensional anisotropy in turbulence. A plausible implication is that these intervals require explicit accounting for plasma and wave speeds when interpreting spacecraft data, rather than simple reliance on the classic Taylor hypothesis (Chhiber et al., 2019, Venzmer et al., 2017).

7. Comparison to Empirical Solar Wind Models

Empirical fits based on OMNI and Helios data model key parameters as lognormal distributions with medians and means scaling with sunspot number (SSN) and heliocentric distance $r$:

• $$B_{\text{med}} = [0.0131\,\mathrm{SSN} + 4.285]\;r^{-1.662}$$
• $$n_{\text{med}} = [0.00381\,\mathrm{SSN} + 4.495]\;r^{-2.114}$$
• $$T_{\text{med}} = [197.4\,\mathrm{SSN} + 5.729\times10^4]\;r^{-1.100}$$
• $v_{\text{med}}$ from a two-component lognormal (slow/fast wind)

At $r=0.046$ AU, $B_{\text{med}}=943$ nT; $v_{\text{med}}=290$ km/s; $n_{\text{med}}=2950$ cm$^{-3}$; $T_{\text{med}}=1.93\times10^6$ K (for SSN$\sim110$ as forecast for late 2024).

The empirical model over-predicts $v$ and $T$ below $\sim20\,R_\odot$, in contrast to MHD+turbulence results and remote-sensing data, which suggests ongoing acceleration and heating. This discrepancy is anticipated and is expected to be resolved by direct PSP measurements, furnishing the first rigorous constraints for refining both theoretical and empirical solar wind models in the near-Sun environment (Venzmer et al., 2017).