the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 21 Feb 2025
Are drivers of northern lights in the ionosphere?
Abstract. We modeled an auroral arc as a negatively charged solitary potential area created by incident energetic electrons in the polar ionosphere. Those negative potential structures are often called ion holes wherein trapped electron populations are denser at the center than at the rim. When an ion hole becomes a sheet-like structure (auroral arc), shear flows are generated in the arc at a right angle to the arc alignment. Shear flows develop twist motion of the sheet into spiral auroras. To maintain spiral motions in the aurora, electron beams follow the auroral motion. This conjunction infers that ion hole in the collisional ionosphere is auroral driver itself.
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RC1: 'Comment on egusphere-2025-716', Anonymous Referee #1, 11 Apr 2025
Review of the Manuscript „Are drivers of northern lights in the ionosphere?”
by Osuke Saka
It is proposed that negatively charged potential structures are created in the ionosphere by incident auroral electrons. They represent ion holes, since the electron density exceeds that of the ambient ions. A one-dimensional ion hole is considered with respect to an electron distribution such that the electric field maximizes at its rim. Electrons perform an ExB drift in that field. This model is extended to two dimensions to form a sheet-like structure with opposing longitudinal electron drifts. Figures depict related charged particle densities, potentials, and converging electric fields. In Section 4, residual flows perpendicular to the arc alignment are postulated. Due to residual fields, rotations in clockwise and counter-clockwise directions are established. Finally, ion holes are approximated by two-dimensional negatively charged solitary areas in the ionosphere. Leakages of the vertical electric field are postulated to occur below and above the ion hole. Those fields leaking upward and pointing downward are postulated to displace the mirror height of the trapped electrons upward. This way, motions of the ion hole may cause the electron beams to follow drifts of the ion hole and act back on the ionospheric rotational motions. Thus, the author concludes that ion holes are the driver of auroral spirals.
This manuscript causes severe difficulties to the reader for two major reasons, the absence of quantities and the complete omission of electric currents. Interaction along B is regarded as only electrostatic. Strangely enough, literature is being quoted, in which electric currents play a major role, with no effect on this theoretical model. The absence of numbers characterizing the scales of the postulated ion holes makes it impossible to relate them with collisional or gyro scales. If electric current closure had been taken into account, the net charge ion holes would have disappeared. This not being the case, I am unable to follow the subsequent derivations.
Special observations:
The designation of dimensionality is unusual. Line 60 in conjunction with Figure 1 (A) shows consistence with the common usage. The discussion in Lines 60-77, combined with Figures 1 (A,B,C) speaks of sheet-like ion holes extending in X and Y. However, in Line 75 it is “regarded a one-dimensional”.
Lines 128-133 in conjunction with Figure 4 (B) suggest two-dimensionality, since rotations are shown in X and Y. However, line 129 still speaks of a 1D ion hole, and the wording, in Lines 140 and 142 suggests that two-dimensionality refers to altitude, since vertical electric fields above and below the hole or “solitary areas” are being considered.
Lines 78-91 contain a discussion of the energy content of the electric field for a 1D ion hole with three different distributions of the two charges. It remains obscure how the different energy contents in Figure 2 are calculated according to Equation 1.
Line 121: What does “residual” mean in residual flows? Does it mean secondary flows? Furthermore, gradients of the magnitude of the drift electric field in the direction of the drift are claimed to exist, but not motivated.
Line 126: “out of these regions” probably means “outside”. Or not?
Lines 128- 135: I am completely lost, since Figure 4 (A) shows the potential only in the X-dimension, i. e. transverse to the arc. However, Figure 4 (B) shows distortions of the principal axis in X and Y, with no potential distribution being presented in X and Y. It makes it impossible to understand the meaning of that figure. On the other hand, what is drawn in that figure, is the basis of the following discussion, in particular with respect to the formation of twists. What does the twist of an axis mean, if the charge density distribution in the X and Y plane is completely missing?
Lines 140-151: Here the ion holes appear as finite along B. I tried to understand what is meant with “leakage” of the electric field. Up to here, no vertical fields were mentioned. However, suddenly, in lines 142-144, a global current circuit is being mentioned without a consideration of the divergences of the field-aligned and transverse currents. If taken into account, it would kill the postulated ion holes. All what follows in this section escapes my understanding. I am just taking note of what is written about feedback between the ionospheric arc and the mirror height of the precipitating electrons. It seems to be the goal of the paper to demonstrate that this feedback couples the horizontal motions in the ionosphere to those of the incident electrons. Here appears what is asked in the title of the manuscript, namely that auroral spirals are driven by the ionosphere.
Conclusion: The formation of ion holes of macroscopic scale by the precipitation of auroral electrons is in severe conflict with the existence and continuity of electric currents and the existence of conductivities and resistances. By neglecting the reality of electric currents, the structures, motions, and deformations of the ion holes are solely subject to electrostatic interactions. However, these interactions lack quantitative definitions. The qualitative descriptions are confusing with respect to their dimensionality. Appearing as structures in a flat ionosphere, their motions and deformations are not controlled by the world above. On the other hand, towards the end of the manuscript, feedback between ionospheric motions and fields and the precipitation of the auroral electron is being claimed, even forming auroral spirals. All of this is contrary to the common understanding of the auroral ionosphere. I wonder how the author was could neglect the action of electric currents in view of the referenced literature. Although receiving an answer would be interesting, I recommend rejecting the manuscript.
Citation: https://doi.org/10.5194/egusphere-2025-716-RC1 -
AC1: 'Reply on RC1', Osuke Saka, 22 Apr 2025
Reply to referee comments RC#1
In this reply, we attempt modeling of (1) field-aligned currents arising from ion hole and (2) two-dimensional motion of the ion hole axis. We also note and respond to other comments. Figures (a,b,c, and d) are in Supplement.
Spatial scale of the ion hole
The size of local aurora (1 km) exceeds gyro-radius of both ionospheric cold ions (O+, 4 m, Ti=0.1eV) and secondary electrons (0.7 m, 100 eV). However, ion gyration could be interrupted by the ion-neutral collisions in the ionosphere because ion-neutral collision frequency exceeds ion-gyro frequency. As a result, collisional ions converge to the negatively charged regions to form solitary potential structures. This may occur independent of the scale size of the potential. We used dimensionless scales to reproduce ion hole motions in Figures 1, 2, 3, and 4. We expect rotational symmetry of spirals between the local and global patterns.ExB drift of the ion hole axis
Figure a(A) shows 2D distribution of ion hole potential Φ(x,y) in X-Y plane. Φ(x,y)=0 outside of the ion hole. Potential profiles along Y component are presented at five different locations in X. Because of converging electric fields along the principal axis, the negative peak at the center of Y increases toward the center of X. Drift of electrons in ion hole marked by arrows in black can be written by Ey(x)/B. Here, Ey(x) is calculated from Φ(x,0)/L. Φ(x,0) is ion hole potential along principal axis. L is half width of the minor axis of the sheet. Non-uniform drifts parallel to the principal axis turn to perpendicular drifts (Vy(x)) as illustrated in Figure a(B) by red arrows. These perpendicular flows deform the ion hole.
The Vy(x) can be written as,
Vy(x)=1/B*(Φ(x+Δx/2,0)/L-Φ(x-Δx/2,0)/L) (1)
and,
~1/(L*B)* dΦ(x,0)/dx*Δx. (2)
Here, B denotes field magnitudes in the ionosphere, Δx is separation distance of the drift circles, and dΦ(x,0)/dx denotes converging electric fields along the principal axis, Ex(x,0).
It is clear that residual flows (Vy(x)) are equal to ExB drift of the principal axis in converging electric fields. The ExB drift patterns of the principal axis illustrated in Figure b(B) (corrected version of Figure 4) are a proxy for deformation processes of the ion hole. It is assumed that space charge fields remain and unchanged in the ion hole during deformation.
Free energies of the ion hole
Space charges redistribute themselves in the ion hole to minimize entire free energies. Entire free energies may be distributed along three degrees of freedom, viz., principal axis, minor axis, and vertically. Electric fields along the principal axis generate meandering motions of the auroral arc through ExB drift. To minimize the relevant free energies along the principal axis, space charges redistribute as demonstrated in Figure 2. Integration is performed along the principal axis. This condition could be applied to the minor axis, but not vertically, because there are charged particles going in and out along the field lines.Vertical electric fields from the ion hole
The vertical component of the electric fields arising from the ion hole impact space weather. Firstly, we observe simultaneous decrease of atmospheric electric fields and ground magnetic field intensity [Saka, 2021]. Correlations infer that vertical electric fields arising from the ion hole affect pre-existing atmospheric potentials that are yielded by charge separation processes in tropical convective storms. Current intensities in this circuit are of the order of pA/m2
Secondly, vertical electric fields above the ionosphere displace mirror height of trapped electrons. Charge separations created by the displaced mirror height yield parallel electric fields in the magnetosphere [Saka, 2023]. They are steady-state electric fields sustained by temperature anisotropies of trapped ions and electrons in the magnetosphere [Alfven and Falthammar, Cosmical Electrodynamics, 1963]. Two types are proposed, upward and downward electric fields arising from negative and positive charges in the ion hole, respectively.Field-aligned currents arising from the ion hole
Ionospheric currents carried by ion drifts in the converging electric fields of the ion hole close via upward and downward field-aligned currents. Ion drift (Ui_perp) may be given as,Ui_perp=Ωi/(B*2π*fin)Ep. (3)
Here, Ωi, 2π*fin, Ep denote ion cyclotron frequency, ion-neutral collision frequency and converging electric fields, respectively. Substituting mean ion cyclotron and ion-neutral collision frequencies, we have ion drift velocities on the order of 5.9*10^1 m/s for electric fields of the order of 0.1 V/m. Those drifting ions carry Pedersen currents of the order of 1.0μA/m2 in the ionosphere (ni=1.0*10^11/m3). These ionospheric currents might be redirected to the field-aligned currents. We therefore suggest that field-aligned currents of the order of 1.0μA/m2 flow above the ionosphere.
We assume that plasmas are collisionless above 140 km in altitudes because both electron- and ion-gyrofrequencies exceed electron-neutral and ion-neutral collision frequencies, respectively. Field-aligned currents arising from the ion hole are calculated by the following relation,J_para=nq*Integral[v_para*f(v, Φ)]*d3v. (4)
Here, f(v, Φ) is the Maxwell distribution function for velocity distributions of ions and electrons, Φ representing field line potential. In the ion hole, downward currents are carried by upward ionospheric electrons from the rim through the loss-cone. Altitude profiles of the downward electric fields and of downward current are presented in Figures c(A) and (B), respectively ranging from 231 km to 5005 km. Background electron density, ne, is assumed to be 1.0*10^8m-3. Current intensity at any point of B increases with electron temperature (Te=1.0eV, 10eV, 100eV, and 1keV) but is insensitive to the potential drop.
From the center, upward currents are carried through the loss-cone by upward ionospheric ions as well as downward plasma sheet electrons through straight-through trajectories. Altitude profiles of the upward electric field amplitudes and of upward current intensity are presented in Figures d(A) and (B), respectively. Background ion density (ni) is assumed to be 1.0*10^11/m3. Ion current intensity at any point of B increases with increasing ion temperature (Ti=0.1eV, 1eV, and 10eV) but once again is insensitive to the electric field amplitudes. Plasma sheet electrons (Te=1keV, ne=1.0*10^6/m3) carry upward currents as well (black line in Figure d(B)). At any point of B, plasma sheet currents increase with increasing potential drop; j_para/v_parq=6*10^-10S/m2 at 950 km consistent with Lyons-Evans-Lundin constant.In the ion hole, Pedersen currents driven by converging electric fields may close via field-aligned currents, upward at the center and downward at the rim. Downward currents are carried by ionospheric electrons and upward by ionospheric ions. It is supposed that plasma sheet electrons precipitating the ionosphere may partly contribute to the current closure via field-aligned currents. Precipitating electrons contribute to production of ion hole in the ionosphere. When precipitation stops, the ion hole may quickly disappear because ion drifts in the ion hole constantly neutralize the secondary electrons produced by precipitations. Number densities of cold electrons carrying downward currents are small as compared to ionospheric ions carrying upward currents. This difference suggests that downward current regions are from “auroral ionospheric cavity” [Doe et al., JGR, 1993].
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AC1: 'Reply on RC1', Osuke Saka, 22 Apr 2025
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RC2: 'Comment on egusphere-2025-716', Anonymous Referee #2, 12 Jun 2025
The manuscript gives a theoretical hypothetical analysis for the ionospheric mechanism of aurora borealis. It is not backed up by any observational material, but that is not really a problem, since the manuscript is clearly presented as a theoretical hypothesis (for instance by the title in the form of a question). Experimental verification of the hypothesis can be done in a separate work.
The description of the theory is not the easiest to follow, but is not impossible either for a reader familiar with the subject.
The only thing that in my opinion is missing from the manuscript, is a quantitative analysis, indicating the estimated strength of the described effect of the ion holes causing the northern lights, with respect to the commonly considered effect of ionospheric electric currents. I noticed that a reviewer already pointed this out in RC1, and the author gave some quantitative estimates in their reply RC2. In my option, it would be good if (some of) this quantitative analysis would be included in the paper, particularly aiming at estimating the strength of the described mechanism, and possibly relative to other mechanisms.
Citation: https://doi.org/10.5194/egusphere-2025-716-RC2 -
AC2: 'Reply on RC2', Osuke Saka, 18 Jun 2025
Reply to referee comments RC#2
We present some quantitative analyses of our auroral model focusing on generation of parallel electric fields in the pre-activated magnetosphere. Figures (A1, A2, and A3) are contained in Supplement.
We assume that charge separation along field lines happens above the polar ionosphere in association with the dipolarization onset [Saka, 2023]. However, parallel electric field arising from charge separation may not be neutralized but instead remain in a steady state if the pitch angle of electrons and ions does not agree [Persson, 1963]. We show that mismatch of pitch angle of electrons and ions occurs.
Pitch angle is modified by the parallel potential arising from the charge separation [Persson, 1966],
sin^2(α)=B/Br (1+qeΦ/(mv^2/2)). (1)
Here, α denotes pitch angles at field magnitude B, Br is field magnitudes at the mirror height (sin^2(α)=1), Φ is field line potential at B, mv^2/2 is kinetic energy of the particle at B, q=1 for ions and q=-1 for electrons, e is a charge.
Effects of the second term of the right-hand side of the equation (1) bring about disagreement of the pitch angle of electrons and ions at any point of B.
The steady-state parallel potentials producing upward electric fields are presented in Figure A1 from 0 km to 10000 km above the polar ionosphere.
Parallel potential yields temperature anisotropy (T_perp/T_para) of trapped electrons and ions. Parallel (T_para) and perpendicular (T_perp) temperatures are calculated by
T_para,perp=m/2*∫d3v [v_para,perp^2*f(v, Φ)] /∫d3v f(v。Φ). (2)
Integration occurs over the velocity space occupied by the trapped electrons or ions. Here, f(v, Φ) is the Maxwell distribution function for velocity distributions of ions and electrons with Φ representing field line potential.
In the case of upward electric fields, perpendicular temperature anisotropy of electrons is enhanced, while for ions, parallel anisotropy increases above the polar ionosphere (Figure A2). This relation reverses for the downward electric fields. In mirror geometry, temperature anisotropies of trapped particles sustain steady-state parallel electric fields in quasi-neutral condition [Alfven and Falthammar, 1963].
We suppose that midnight magnetosphere, referred to as the pre-activated magnetosphere, develops temperature anisotropies of trapped plasma sheet particles at the dipolarization onset. When such anisotropies resolve for whatever reason by filling loss-cone with plasma sheet particles, only those in limited velocity space can reach the ionosphere as precipitation. For the upward electric fields, trapped electrons with low kinetic energy cannot reach the ionosphere. Consequently, trapped electrons reaching the ionosphere as precipitating electrons increase their kinetic energies. Energization of precipitating electrons is proportional to the parallel potential imposed on the midnight magnetosphere (Figure A3). In contrast, trapped ions are not energized by the upward electric fields but precipitate thermally in the ionosphere. In the pre-activated magnetosphere, field-aligned currents are carried by particles of the ionospheric origin. Field-aligned currents of magnetospheric origin initiate in association with the breakdown of the temperature anisotropy.
References
Alfven, H. and Falthammar, C.-G.: Cosmical Electrodynamics, 2nd ed., Oxford University Press, New York, 1963.
Persson, H.: Electric field along a magnetic line of force in a low-density plasma: Phys. Fluids, 6, 1756-1759, 1963.
Persson, H.: Electric field parallel to the magnetic field in a low-density plasma: Phys. Fluids, 9, 1090-1098, 1966.
Saka, O.: Parallel electric fields produced by ionospheric injection, Ann Geophys., 41, 369-373, 2023.
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AC2: 'Reply on RC2', Osuke Saka, 18 Jun 2025
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