**3. Geomagnetic modulation of charged particles in Earth's atmosphere**

#### **3.1 Van Allen radiation belts**

Important structures in Earth's magnetosphere are its radiation belts, which consist of relativistic electron and proton populations, trapped in the Earth's magnetic field. The Earth has two such belts and some others may be temporarily created. The *outer* radiation belt, occupying the space between 3 and 10 Earth's radii (RE), consists mainly of electrons with energies 0.1–10 MeV (million electron volts). The outer belt's particles have both – solar (mainly helium ions) and atmospheric origin. The protons of the *outer* belt, however, possess much lower energies than those of the *inner* belt. The most energetic particles of the outer belt are electrons, achieving energies of several hundred MeV.

An electrons population is found also in the outer edge of the *inner* radiation belt at a distance 1.5÷3 RE [42]. The outer and inner electrons' belts are separated by the *slot* region, where the interactions with the electromagnetic waves called "whistlers" are the main reason for the lower density of the electron population. The electrons' loss in the slot region is due to the pith angle scattering (related to the impact of whistlers) – facilitating their escape from the geomagnetic trap [43]. The inner belt electron population is periodically refreshed by the transport of electrons from the outer radiation belt [44]. Moreover, it has been recently recognized that the decay of thermal energy neutrons, produced by cosmic rays striking the upper atmosphere, contributes to energetic electrons in the inner belt and acts as the dominant source of energetic electrons at the inner edge of the inner belt [45].

The *inner* radiation belt, occupying the near Earth space between 0.2 and 2 RE, is largely populated, however, by energetic protons with energies exceeding 30 MeV. According to the current understandings, these protons originate from: (i) the decay of neutrons – produced within the interaction between galactic cosmic rays and atmospheric atoms and molecules [46], and (ii) solar protons – injected into the interplanetary space during the solar flares and coronal mass ejections [47–49]. The solar energetic protons are the primary source of particles for the inner belt, which energy is beneath �100 MeV [49] and sometimes produces a long-lived proton belt – distinct from the inner radiation belt [47, 50].

#### **3.2 Particles' focusing in a heterogeneous magnetic field**

Particles trapped within the geomagnetic field are urged by the Lorentz force (1) to move along the magnetic field lines on spiral trajectories (the result of a combined *circular* and a *field align* motions), continuously bouncing between the Northern and the Southern Hemispheres.

$$\mathbf{m}\frac{\mathbf{dv}}{\mathbf{dt}} = \mathbf{q}[\mathbf{E} + (\mathbf{v} \times \mathbf{B})]; \mathbf{v} = \frac{\mathbf{dr}}{\mathbf{dt}}\tag{1}$$

where: B(r,t) is external magnetic field – function of the spatial dimensions and time, r and v are respectively particle's radius vector and velocity; "m" is particle's mass and "q" – its charge.

Besides the helical movement of particles along geomagnetic field lines, they also perform the additional movement in a direction perpendicular to the magnetic field

lines – known as *magnetic drift*. This type of motion is determined by the nonuniformity of Earth's magnetic field in the direction perpendicular to B, and by the magnetic field curvature (2)

$$\mathbf{v}\_{\rm drift} = \frac{\mathbf{m}}{\mathbf{q} \cdot \mathbf{B}^2} \left( \mathbf{v}\_{\perp}^2 \frac{\mathbf{B} \times \nabla \mathbf{B}}{2\mathbf{B}} + \mathbf{v}\_{\rm II}^2 \frac{\rho \times \mathbf{B}}{\rho^2} \right) \tag{2}$$

where B is the magnetic vector, ρ – the radius of the geomagnetic lines curvature, vII and *v*<sup>⊥</sup> are projections of particle's velocities parallel and perpendicular to geomagnetic field line; q and m are respectively particle's charge and mass. The first term in the brackets corresponds to the magnetic gradient perpendicular to the field lines, while the second term – to their curvature.

Formula (2) shows also that particles' drift across the magnetic field lines depends on their charge q, and consequently leads to a charge separation, which in turn generates electric field E along the drift direction. The combined effect of E and B fields induces an E�B/B<sup>2</sup> drift of particles, which displaces positive ions and negative electrons in the same direction – perpendicular simultaneously to B and to E. These charged particles are then "lost" in the ambient atmosphere, where they release their energy, producing showers of secondary particles.

In a dipolar geomagnetic field (with its cross-latitudinal magnetic gradient) the protons are drifting westward, while electrons – eastward. The real geomagnetic field has, however, a non-dipole component creating additionally a cross-longitudinal gradient. In this case, the protons (entering the denser atmosphere from the west) are shifted sought-westward in regions with a positive cross-longitudinal gradient and sought-eastward – in regions with a negative gradient (refer to Eq. (1)). Consequently, the overall westward drift (forced by the magnetic curvature and crosslatitudinal gradient) is reduced by the eastward component – exerted in regions with a negative azimuthal magnetic gradient. Furthermore, the electric field (induced by the charge separation of impending particles) is significantly reduced in these regions. Finally, the number of particles expelled outside the magnetic trap (due to the (E � B)/B<sup>2</sup> electric drift) is much less. More precisely, only a few of them have a "chance" to be lost in the atmosphere in said regions.

Oppositely, in regions with positive azimuthal geomagnetic gradients, the southward drift component changes slightly in the direction, but not the amplitude of the westward drift, impelled by the magnetic curvature and latitudinal gradient. Consequently, in these regions, the induced electric field – resulted from the charge separation of arriving particles – is much stronger. It will intensively expel the charged particles outside the magnetic trap through the imposed (E � B)/B<sup>2</sup> drift. Furthermore, these particles interact with the atmospheric molecules creating secondary electrons, ions, and nuclear products, giving rise to the ionization of the lower atmosphere.

### **3.3 Hemispherical asymmetry of geomagnetic non-dipolar field and its influence on particle precipitation in Earth's atmosphere**

The confinement of any particle in the gradient magnetic field B depends on the ratio between the maximum field strength Bmax in the polar regions (where the backward reflection of trapped particles occurs) and the equatorial magnetic field strength B0, i.e.

*Coupling between Geomagnetic Field and Earth's Climate System DOI: http://dx.doi.org/10.5772/intechopen.103695*

$$
\sin\left(a\right) = \sin\left(a\_0\right) \cdot \sqrt{\frac{B\_{\text{max}}}{B\_0}}\tag{3}
$$

where the angle α<sup>0</sup> between velocity vector of arriving particle and corresponding magnetic line in the equatorial region, is known as an equatorial *pitch* angle, and α is the continuously changing pitch angle, when particle is moving along the magnetic field line. Thus *α* increases with particles' movement toward the pole, due to the reduction of filed aligned component of particles velocity, and increase of its velocity in a direction perpendicular to geomagnetic field line (refer to formula (4) and **Figure 4**), are decreases when particle is moving toward the equator.

$$a = 2\pi \left(\frac{\mathbf{v}\_{\mathrm{II}}}{\mathbf{v}\_{\mathrm{L}}}\right) \cdot \mathbf{r}\_{\mathrm{B}}, \quad \text{where } \mathbf{r}\_{\mathrm{B}} = \frac{\mathbf{m}}{\mathbf{q}\mathbf{B}} \ \mathbf{v}\_{\mathrm{L}} \tag{4}$$

Any particle is assumed trapped by the magnetic field, when the angle *α* becomes greater than *<sup>π</sup>* <sup>2</sup>, because at this point – known as a magnetic mirror – the particle reverses its direction of movement, remaining confined by the magnetic field line. Formula (3) shows that particles approaching Earth's magnetosphere at very small angles could not exceed the pith angle *<sup>π</sup>* <sup>2</sup>, and when enter the mirror point these particles are "lost" in the atmosphere. The minimum value of angle *α*0*<sup>m</sup>* (for which the maximum magnetic field is still able to reflect particles) is called *loss cone*. If a particle arrives at angle lower than the solid angle defined by α0m, it will be lost in the ambient atmosphere on its motion along the magnetic field line. Formula (3) shows also that the efficiency of magnetic mirror to reflect charged particles does not depend

#### **Figure 4.**

*Orientation of the particle's velocity vector, with respect to the equatorial magnetic field B0, and changing particles pitch angle α (from α<sup>0</sup> at the equator, to 90 degrees at magnetic mirror point).*

neither on the particles speed, nor on their charge and mass (in the guiding center approximation, known also as adiabatic approximation).

The geomagnetic field near the poles is stronger in the Southern Hemisphere, compared to those in the Northern Hemisphere. Consequently, in the case of isotropic particles' flux arriving at magnetopause – almost every third particle will be confined in the Southern Hemisphere, while in the Northern Hemisphere less than ¼ of all arriving particles are trapped, because of its larger loss cone [51]. This means that some of particles confined in the Southern Hemisphere could not be held by the weaker geomagnetic field in the Northern Hemisphere. The expected result is – more particles precipitating in the Northern Hemisphere.

## **3.4 Regener-Pfotzer maximum and its influence on the lower stratospheric chemistry**

Energetic particles penetrating deeper in the atmosphere create showers of secondary particles, produced from their interaction with atmospheric molecules – the deeper the penetration is, the wider the showers are. In the lower stratosphere, the number of secondary products dramatically increases, becoming maximal at a certain level. This level is known as a Regener-Pfotzer maximum. Beneath it, the concentration of secondary ions and electrons decreases again.

The longitudinal geomagnetic gradient and hemispherical asymmetry of geomagnetic field determine the uneven distribution of geomagnetically trapped particles' precipitation over the globe (refer to Subsections 3.2 and 3.3). Existence of such an effect is illustrated in [52].

#### *3.4.1 Ozone formation in the lower stratosphere*

For almost a century –since the creation of the theory about ozone production in the upper atmosphere by Sydney Chapman [53] – the single source of stratospheric ozone is believed to be the photo-dissociation of molecular oxygen by solar ultraviolet radiation. Recently it has been shown that in the dry lowermost stratosphere the lower-energy electrons in the Regener-Pfotzer maximum initiate ion-molecular reactions producing ozone [54].

The mean energy of electrons in the Regener-Pfotzer max (�35 eV [55]) is not sufficient to break the molecular bounds of the major atmospheric constituents. It is, however enough to ionize the molecular oxygen (Reaction (5)). The oxygen cation interacts furthermore with neutral oxygen molecule, producing a tetra-oxygen ion O<sup>þ</sup> 4 [56, 57], (see Reaction (6)).

Being very unstable, this oxygen complex rapidly dissociates into two different channels [57]. The first channel (7) produces O<sup>þ</sup> <sup>3</sup> and *O*, while the second one restores the O<sup>þ</sup> <sup>2</sup> ions (8). The weakly bonded O<sup>þ</sup> <sup>3</sup> molecule easily dissociates or exchanges its charge with O2, yielding a neutral ozone. Most efficient, however, appears to be the dissociative recombination of ozone cation O<sup>þ</sup> <sup>3</sup> to three oxygen atoms, occurring in 94% of all cases [58], in prevailing conditions typical for the lower stratosphere (i.e. ground state ozone cations and lower energetic electrons).

$$\text{O}\_2 + \text{e}^- \rightarrow \text{O}\_2^+ + 2\text{e}^- + 12.07\text{ eV} \tag{5}$$

$$\text{O}\_2^+ + \text{O}\_2 + \text{M} \rightarrow \text{O}\_4^+ + \text{M} + \text{3.5 eV} \tag{6}$$

*Coupling between Geomagnetic Field and Earth's Climate System DOI: http://dx.doi.org/10.5772/intechopen.103695*

$$\rm O\_4^+ \rightarrow \rm O\_3^+ + \rm O + 0.82 \, eV \tag{7}$$

$$\text{O}\_4^+ \rightarrow \text{O}\_2^+ + \text{O}\_2 + \text{1.26 eV} \tag{8}$$

$$\text{O}\_3^+ + \text{M} \rightarrow \text{O} + \text{O} + \text{O} + \sim \text{0 eV} \tag{9}$$

$$\rm O + O\_2 + M \rightarrow O\_3 + M \tag{10}$$

$$\text{Net}: \text{1O}\_4^+ \to \text{4O}\_3 \tag{11}$$

As a result, the dissociation of one *O*<sup>þ</sup> <sup>4</sup> molecule leads to the formation of four new O3 molecules (reactions (7) and (9)), while reaction (8) and continuous ionization of O2 by the atmospheric lower-energy electrons support a steady production of *O*<sup>þ</sup> 4 (more detailed analysis could be found in [51, 53]. Thus, the reactions (6)–(9) form an autocatalytic cycle for continuous O3 production in the lower stratosphere. An absolutely necessary condition for the activation of autocatalytic ozone production is a dry atmosphere. Otherwise, water clusters of *O*<sup>þ</sup> <sup>2</sup> are formed instead of *O*<sup>þ</sup> <sup>4</sup> [59]. The maximum efficiency of this ozone-producing cycle should be expected near the level of the highest secondary ionization produced by GCRs, i.e. near the Regener–Pfotzer maximum.
