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tokens: to interval E4, as well as the full spectrum irrespective of the angle. The spectral break between the 1∕ f and f −3∕2 ranges for the unconditioned spectrum (black line) is found approximately (by inspection) at f b ≈ 2 × 10 −3 Hz, indicated by the vertical dotted line. Right : spatial energy spectrum of magnetic fluctuations E ( k ⊥ ) reconstructed from the frequency spectra P sc ( ω , θ VB ) for each sampling angle as well as by using the standard TH (black line). 4.2 Reconstructing field-perpendicular spectrum E(<italic>k</italic><sub>⊥</sub>) In the following, we proceed to reconstruct the reduced energy spectrum E ( k ⊥ ) using data from within each angle bin above 30° and for which we find a large statistical sample. For illustration purposes, we concentrate on a 24 h interval just before the fourth perihelion (E4), which was also investigated using standard TH analysis by Chen et al. (2021) . Table 3 shows the values of ε , V ⊥ , and the number of statistical samples (counts) associated with this interval for each ten-degree angle bin around 30°, 40°, 50°, and 60°. In this statistical sample, ε ≤ 0.2, in which case the BP19 methodology in the TH limit ( ε → 0) is applicable, that is, combining Eqs. ( 2 ) and ( 3 ) leads to The most common form of TH follows from this expression by performing the integral in a Cartesian coordinate system with one axis along the streamwise direction so that Here E 1 D ( k s ) is the one-dimensional energy spectrum with respect to the streamwise (sampling) direction. This expression resembles Eq. ( 6 ) with Λ α , ε = 1 and leads to the familiar ω = − k s V expression to relate spacecraft frequencies with streamwise wavenumber k s . Table 3 Relevant parameters for each angle bin considered in our analysis with a sufficiently large number of samples. Notes. The parameter ε remains below 0.15, which allows for the application of the TH in the framework of BP19. For reference, at 1 s resolution, the total number of counts in any given 24 h interval is 86 400 samples. It is also important to note that values for Λ α , ε were calculated for α = 3∕2 and using Eq. ( 18 ) Λ TH ≃ 0.7628. However, because we are interested in reconstructing the angle-integrated field-perpendicular spectrum E ( k ⊥ ), Eq. ( 16 ) must be integrated in cylindrical coordinates. Using the change of variables x = ω ∕ k ⊥ V ⊥ , we obtained 3 where Again, Eq. ( 18 ) also resembles Eq. ( 6 ) with Λ α , ε replaced by Λ TH . In fact, it can be shown that , which is consistent with the BP19 model in the limit when ε → 0. The scaling factor Λ TH is due to the integration with respect to the angle φ in the dot product k ⊥ ⋅ V = k ⊥ V ⊥ cos φ ( Bourouaine et al. 2012 ; Bourouaine Chandran 2013 ; Martinović et al. 2019 ). Using Eqs. ( 11 ) and ( 12 ) within each statistical sample described in Table 3 , P sc ( ω , θ V B ) was calculated for magnetic field measurements b ( t ) according to Eq. ( 12 ). The left panel of Fig. 3 shows frequency spectra P