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Home , Explorer 4, Pioneer 3, Van Allen radiation belt

Copyrights Prof Marko Popovic 2021

Magneto Freshmen physics: charge in magnetic field

In the plane perpendicular to field lines the 푞 > 0 풗 rotates around the field B lines with “constant” speed (magnetic force 푚 is always perpendicular to particle velocity) and radius can be obtained as follows: 푅 푚푎Ԧ = qv × 퐵

푣2 푚 = 푞푣퐵 푅 B Larmor radius 푚푣 2푅휋 2휋푚 1 푅 = with period of rotation 푇 = = = 푞퐵 푣 푞퐵 푓 Uniform magnetic field (independent of speed) 퐶

Small print disclaimer: the accelerating charged particle radiates electromagnetic waves and hence looses kinetic In the uniform magnetic field

The cyclotron frequency

fC is only function of 퐵 Component of velocity 푞 Component of and ratio. perpendicular to 퐵 is velocity parallel 푚 rotating (but speed is to 퐵 is constant. constant). For example, if we have twirling around the 0.1 푇 field lines (say inside a sunspot) we expect with cyclotron frequency of roughly

2휋푚 2휋 × 9.109 × 10−31푘푔 1 푇 = 푒 = ≈ 3.57 × 10−10푠 → 푓 = ≈ 2,800 푀퐻푧 푒퐵 1.602 × 10−19퐶 0.1푇 푇

Hence, no surprise that there is a superb correlation between the number of sunspots and the intensity of ퟐ, ퟖퟎퟎ 푴푯풛 radiation. How about incoming charged particles and ’s magnetic field?

−5 Average magnetic field on the surface of the Earth is about 퐵ത 푅퐸 ≅ 3.1 × 10 푇 At roughly half the Earth’s radius above the Earth’s surface, magnetic field is about 10−5푇. What is the Larmor radius of an isolated moving with 푣 = 400 푘푚/푠 (typical Solar speed)? Result depends on the angle between proton’s velocity and B field, but it should be less than −27 5 푚푝푣 1.673 × 10 푘푔 4 × 10 푚/푠 푅 = = ≅ 4.2 102 푚 = 420 푚 tiny 푒퐵 1.602 × 10−19퐶 10−5푇

Performing same calculation for an , which is roughly 2,000 times lighter than proton, gives 2,000 times smaller radius of rotation, or about 21 푐푚. How important is gravity for these particles?

Let’s compare magnetic and gravitational forces

푚 푒푣퐵 = 1.602 × 10−19퐶 × 4 × 105 × 10−5푇 = 6.4 × 10−19 N 푠 and −27 2 푀퐸푚푃 푚푃푔 1.673 × 10 푘푔 × 9.81푚/푠 −27 퐺 2 = 2 = = 7.3 × 10 N 1.5 푅퐸 1.5 2.25 for proton (for electron is ~3.6 × 10−30 N).

Hence, yes, it’s all about the magnetic field. Hence, both and electrons appear tightly stuck to Earth’s magnetic field lines. And Earth’s magnetic field acts as an “umbrella” against ’s charged particle “rain”. It protects us!

But we need to be careful here… our calculation assumed isolated incoming particles. But there are many incoming particles and they also carry their own magnetic field…plus there are extreme events like massive Coronal Mass Ejections (CME) and catastrophic geomagnetological storm they may cause…

That can be a problem. We will address that later.

Let’s first discuss our everyday magnetic “umbrella” a bit more. What generates this magnetic field? The Earth’s magnetic field

Scientific literature typically states that the Earth’s magnetic field is generated by convective motions within its molten outer core. (we will return to this in a moment) The Earth’s structure is represented with hot and massive Core (푇 = 5,000 퐾), rich in iron and nickel, which occupies 16% volume and it contributes 31% mass. Inner Core (0 − 1300 푘푚) is solid (high pressure) and Outer Core (1300 − 3550 푘푚 ) is liquid (low pressure). They are followed by rocky Mantle (3550 − 6450 푘푚), rich in heavy elements like iron, and then by thin rocky Crust (thickness between 8 and 40 푘푚), rich in light elements like silicon and aluminum. Of course, none have ever drilled a deep enough hole (to the center of the Earth) to directly check these hypotheses (deepest hole is ~12 푘푚). But, these ideas are in a very good agreement with other things we know with much more certainty.

For example, one could study propagation of seismic waves like P (for pressure) and S (for shear) waves and learn a lot on inner Earth. The Earth’s magnetic field

One can measure magnetic field everywhere on the surface on the Earth, perform mathematical analysis, and discern class of magnetic field type. Apparently, more than 90% of observed surface field can be explained with magnetic dipole field. The rest (often called ‘anomaly’) can be explained with higher terms in multiple expansion like quadrupole term, and so forth. One could also show that 99% of surface field has origin within the Earth and less then 1% is of extraterrestrial origin.

Last 4 centuries The Earth’s magnetic field

The center of magnetic dipole does not coincide with geometric center of the Earth (best fit model is 550 km off; causing ) and magnetic NORTH-SOUTH do not exactly coincide with the axis of the Earth’s daily rotations. (see next slide) In terms of geographical location, the magnetic North Pole moves a bit erratically within ~80 km ellipse every day (attributed to extraterrestrial variations) and its mean location is currently speeding at ~50 km/year (btw, it was moving much less only a hundred years ago).

Most popular hypothesis

The Earth's magnetic field is mostly caused by electric currents in the liquid outer core. The Earth's core is hotter than 1043 K, the Curie point temperature above which the orientations of spins within iron become randomized. Such randomization causes the substance to lose its magnetization.

Convection of molten iron within the outer liquid core, along with a Coriolis effect caused by the overall planetary rotation, tends to organize these "electric currents" in rolls aligned along the north-south axis. Convection currents of fluid metal in the Earth's outer core, driven by heat flow from the inner core, organized into rolls by the Coriolis force, create circulating electric currents, which generate the magnetic field Most popular hypothesis

When conducting fluid flows across an existing magnetic field, electric currents are induced, which in turn creates another magnetic field. When this magnetic field reinforces the original magnetic field, a dynamo is created that sustains itself. This is called the Dynamo Theory and it “explains” how the Earth's magnetic field is sustained.

NOT YET PROVEN; not even as an computer simulation model

Convection currents of fluid metal in the Einstein thought it is wrong; he believed Earth's outer core, driven by heat flow from that Earth has excess charge the inner core, organized into rolls by the Coriolis force, create circulating electric currents, which generate the magnetic field Coriolis force is fictitious force in non-inertial rotating frame. 휔

퐹Ԧ퐶표푟푖표푙푖푠 = −2푚 휔 × 푣Ԧ′ 푟Ԧ = 푟0 + 푟′

푑푟Ԧ 푑푟 푑푟Ԧ′ 푑푟 푑푟Ԧ′ = 0 + ቤ = 0 + ቤ + 휔 × 푟′ 푑푡 푑푡 푑푡 푑푡 푑푡 푆 푆′

푑2푟Ԧ 푑2푟 푑2푟Ԧ′ 푑푟Ԧ′ 푑 휔 × 푟′ = 0 + อ + 휔 × ቤ + + 휔 × 휔 × 푟′ 푑푡2 푑푡2 푑푡2 푑푡 푑푡 푆′ 푆′

푑2푟Ԧ′ 푑2푟Ԧ 푑2푟 푑휔 푑푟Ԧ′ 2nd Newton Law 푚 อ = 푚 − 푚 0 − 푚 × 푟′ − 푚2 휔 × ቤ − 푚휔 × 휔 × 푟′ 푑푡2 푑푡2 푑푡2 푑푡 푑푡 in non-inertial 푆′ 푆′ rotating frame Real physical force Coriolis force Magnetic field reversal

A is a change in a 's magnetic field such that the positions of magnetic north and magnetic south are interchanged.

There have been 183 reversals over the last 83 million years (on average once every ~450,000 years). The latest, occurred 780,000 years ago.

The duration of a full reversal is typically between 2,000 and 12,000 years. (!) How is life protected during full reversal? “Good news”: It is believed that the magnetic field will not vanish completely, but many poles might form chaotically in different places during reversal, until it stabilizes again. Some geoscientists believe that inner core also contributes to magnetic field and it is much more stable against perturbations with diffusion timescale of 3Ky vs outer core with 0.5Ky. Some believe that the solar wind can even induce a magnetic field in the Earth's sufficient to shield the surface from energetic particles. The thick atmosphere will also help against bombardment of solar wind particles and high energy cosmic rays. collisions would produce secondary radiation of beryllium- 10 or chlorine-36. (Beryllium-10 discovered in Greenland ice core correlates well with 5% of magnetic field value during one of the recent reversals.) Statistical analysis shows no evidence for a correlation between reversals and extinctions. “Bad news”: We don’t really know. We don’t really know how exactly the Earth’s magnetic field is generated and we don’t really know what exactly happens during large magnetic field excursion or full reversal.

Independent of how the magnetic field is generated, to produce the present field, which is very similar to that of a dipolar bar magnet, the equivalent current should be turning westward.

The Earth’s dipole moment, 휇 = 퐼 × 푎푟푒푎, is equal to 7.95 × 1022 퐴 푚2 . Btw, a 6 loop the size of the liquid core (푅푐 = 3.48 × 10 푚 ) would require an equivalent current of nearly 2.00 × 109 퐴.

Here “westward” refers to observations of an observer at rest in an inertial frame.

Interestingly, if there exists charge separation or perhaps just an excess of negative charge that appear static for an Earth-bound observer, for an observer in an inertial frame this charge will form westward turning current (because of Earth’s rotation) and hence generate magnetic dipole moment oriented toward geographic south. Static charge case Earth spinning

Geographic north

푞 푞 푞 푞 푞 푞 퐼 푞 ------푞- - - - - 푞 푞 푞 푞 푞 퐼

Geographic south For Earth-bound observer For extraterrestrial observer (static charge in non-inertial frame) (westward electric current in inertial frame)

Felt by Earth-bound observer Causes magnetic field (pointing down) Magnetic and geographic poles coincide Static electric current case

Geographic north

Magnetic and geographic poles do not need to coincide.

퐼 Magnetic poles are static on Earth surface.

퐼 But what could cause “chaotic” daily motion of poles?

Geographic south For Earth-bound observer (static electric current in non-inertial frame) Perhaps that is a collective phenomena of many synchronized electrons performing Larmor precession due to the external magnetic field created by the (and perhaps Van Allen belts). Larmor precession (named after Joseph Larmor) is the precession of the magnetic moment of an object about an external magnetic field. Objects with a magnetic moment also have angular momentum and effective internal electric current proportional to their angular momentum; these include electrons, protons, other fermions, many atomic and nuclear systems, as well as classical macroscopic systems. 휏Ԧ = 휇Ԧ × 퐵 = 훾퐽 × 퐵 The angular momentum vector 퐽Ԧ precesses about the external field axis with an angular frequency known as the Larmor frequency 휔 = −훾퐵 where 퐵 is the magnitude of the applied magnetic field, 훾 is (for a particle of charge −푒) the gyromagnetic ratio equal to 푒푔 훾 = − 2푚 where 푚 is the mass of the system undergoing precession, while 푔 is the g-factor of the system. The g-factor is the unit-less proportionality factor relating the system's angular momentum to the intrinsic magnetic moment; in classical physics it is just 1. Let’s imagine that this Larmor frequency is somehow equal to the Earth’s spinning frequency and try to estimate the strength of the external magnetic field that would cause such phenomena.

푒푔 2휋 1.602 × 10−19퐶 휔 = 퐵 → = −31 푔퐵 2푚푒 24 × 60 × 60 푠 2 × 9.109 × 10 푘푔

Classicaly, for 푔 = 1 this hypothesis would predict 퐵 = 0.83 푛푇~1 푛푇 . The same order of magnitude as average observed Sun’s magnetic field ~6 푛푇.

For 푔 = 2 (relativistic electron) prediction is 퐵 = 0.42 푛푇~0.5 푛푇.

Maybe this collective synchronized magnetic field, if it exists, is our second line of defense that is still sufficient during “reversal” and could keep the at two, three Earth’s radii from the Earth? The Earth’s magnetic dipole and Sun’s 퐵 field

If ‘dynamo’ mechanism is not shielded from the Sun’s magnetic field it is worth investigating potential effects of Sun’s magnetic field on Earth’s ‘dynamo’. The energy of dipole in magnetic field is

푈 = −휇Ԧ ∙ 퐵 = −휇퐵 cos 휃

Hence over the period of one day there will be some variability of this energy equal to ∆푈 = −휇퐵 ∆ cos 휃

…and that is quite realistic possibility as magnetostatic shielding is a completely different ‘beast’ than electrostatic and/or electromagnetic wave shielding…especially in conditions without “grounding”  The Earth’s magnetic dipole and Sun’s 퐵 field

Although there is a strong dependence on the time of the year and the location of magnetic pole lets assume ∆ cos 휃 ~0.1.

Average Sun’s magnetic field at 1 AU is ~6 푛푇. Hence

∆푈 = 0.1 휇퐵 = 0.1 × 7.95 × 1022 A/푚2 × 6 × 10−9푇 = 4.77 × 1013퐽

Although this may appear like a lot of energy, it is actually a really tiny energy compared to that of black-body radiation coming from the Sun. It is orders of magnitude smaller than energy of photons arriving each second to the Earth. 푊 1,367 6.371 × 106푚 2휋 1푠 = 1.74 × 1017퐽 푚2 The Earth’s magnetic dipole and Sun’s 퐵 field If ‘dynamo’ is not shielded, Sun’s 퐵 field will also generate torque on dipole 휏Ԧ = 휇Ԧ × 퐵 To estimate magnitude, one could assume sin 휃 ≈ 0.1 such that 휏 = 휇Ԧ 퐵 sin 휃 = 4.77 × 1013푁푚 37 2 The Earth’s moment of inertia about axis of rotation is 퐼퐸 = 7.7 × 10 푘푔푚 . Therefore, angular acceleration is 휏 훼 = = 6.2 × 10−25푟푎푑/푠2 퐼 The time that would be needed to change Earth’s current angular speed by 1% is 휔 0.01 2휋 푟푎푑 푡 = 0.01 퐸 = = 1.2 × 1018푠 ≈ 3.7 × 1010푦 훼 6.2 × 10−25푟푎푑/푠2 24 × 60 × 60 푠 Hence, no worries (Sun’s life expectancy is only 1010푦). Inclinations of orbital planes

The invariable plane of a planetary system, also called Laplace's invariable plane, is the plane passing through its barycenter (center of mass) perpendicular to its angular momentum vector.

The invariable plane is within 0.5° of the orbital plane of , and may be regarded as the weighted average of all planetary orbital and rotational planes. Earth’s magnetic field and solar wind In difference to Sun’s magnetic field (which decreases as 푟−2) the Earth’s magnetic field decreases as 푟−3and can be well described with magnetic dipole field 휇 휇Ԧ 퐵 푟Ԧ = 0 2 cos 휃 푟Ƹ + sin 휃 휃෠ 4휋푟3 where 휇Ԧ is magnetic dipole moment. (For example if there is current loop 휇Ԧ = IA .) Hence, for given 휃, radial dependence can be expressed as

푅3 퐵 푟, 휃 = 퐵 푅 , 휃 퐸 퐸 푟3 where 퐵 푅퐸, 휃 is the Earth’s surface 퐵 field value. We have discussed “magnetic umbrella” and we will specify its location. But let’s first figure out location of “drumhead”. 

Typically in literature, “hard wall” or “drumhead” distance from Earth is obtained by equating energy density of magnetic field with kinetic energy density of solar wind 퐵2 휌푣2 = 2휇0 2

−9 −3 The average kinetic energy density at 1 AU is 휌퐾 ≈ 10 퐽푚 . Hence

1 3 2 2 6 퐵ത 푅퐸 푅퐸 푟 퐵ത 푅퐸 6 ≈ 휌퐾 → = ≈ 8.5 2휇0푟 푅퐸 2휇0휌퐾

This is a rough estimate of distance to the so-called terrestrial magnetopause in the direction of the Sun. The observed magnetopause distance is actually at ퟏퟎ 푹푬. Interpretation of ퟏퟎ 푹푬 is that the Earth magnetic field has enough energy to counteract and completely stop incoming solar wind particles at this distance.

Another interpretation is that this is a “hard wall” boundary that separates Earth’s and Sun’s atmospheres.

Encyclopedia Britannica: “On the dayside of Earth the magnetic field of the planet terminates at a distance of about 10 Re. The boundary that exists at this point is called the magnetopause (break in magnetic field). Outside this boundary magnetic fields and particles are present, but they belong to the Sun’s atmosphere and not to Earth’s.” Earth's Magnetic Field Vibrates Like a Drum (1 min 59 sec) https://www.youtube.com/watch?v=iVSD9x598jw NASA Goddard’s Space Center

NASA’s THEMIS mission proves a 45-year old theory that the outer boundary of Earth’s magnetic field vibrates like a drum. Credit: Martin Archer, Queen Mary University of London

When a plasma jet — the drumstick — strikes the magnetopause, surface waves form a standing wave pattern — where the ends appear to be standing still while other points vibrate back and forth — just like a drumhead. The fixed points in the wave, which are the rim or edge of the drum, are near Earth’s magnetic poles; the waves vibrate the surface of the magnetopause in between. While the wave itself remains on the surface, the vibrations ultimately work their way down into the and trigger other types of waves.

“The waves likely penetrate far into the inner magnetosphere causing ultra-low frequency waves, which affect things like radiation belts, the , and even the ionosphere.” However, one would expect from an “umbrella” to redirect (and not fully stop) incoming particles’ motion.

Let’s look for another 푟 (distance from the Earth) that is also equal to radius of proton’s turning about magnetic field lines (!), i.e.

3 −19 −5 6 푚푣 푚푣푟푝 푟푝 푞퐵ത 푅퐸 푅퐸 1.602 × 10 퐶 3.1 × 10 푇 6.371 × 10 푚 푟푝 = = → = = ≅ 217.5 푞퐵 푞퐵ത 푅 푅3 푅 푚푣 −27 5 푚 퐸 퐸 퐸 1.673 × 10 푘푔 4 × 10 푠

For electrons moving at the same speed (200 푘푚/푠) this radius will be even larger, i.e. 2000 ≈ 44 times larger.

For protons moving at 1600 푘푚/푠 it will be half the value or 109 푅퐸. While for alpha particles moving at the same 1600 푘푚/푠 it will be 109 푅퐸/ 2 ≈ 77푅퐸. For reference Earth distance is 60 푅퐸. 푝+ 훼++ 푝+ 훼++ 푒− 푒− 푝+ 훼++ 푒− 훼++ 푝+ 훼++ 푒− 푝+ 푒− 훼++ 푝+ 푒− 푒− Do we have different “umbrellas” for different particles and for different speeds? Answer is no. This is really a collective phenomena. (!) First of all, particles don’t just get that easily separated from the rest of plasma as there are Coulomb forces that keep particles together; plasma prefers to stay in a globally electrically neutral state. Plasma also carry its own local magnetic field which is stronger than the Earth magnetic field for larger distances from the Earth. Hence particles trajectories are not as simple and they do not match the trajectories of isolated particles in the Earth’s magnetic field. Plasma will approach Earth at much shorter distance then isolated particles. (!) Good news - the solar wind loses its bulk speed while approaching Earth as more and more plasma particles rotate vigorously around Earth magnetic field lines (characterized by greater magnitude at smaller distances from the Earth).

At some distance ~15 푅퐸 plasma speed will transition from “supersonic” to “subsonic” and there will be accumulation of particles in the shock wave. .

At the bow shock, the bulk forward velocity of the wind (which is the component of the velocity parallel to the field lines about which the particles gyrate) drops below the speed at which the particles are gyrating. The Bow shock is actually what we referred to as the “magnetic umbrella” (at least in a sense of how it appears) and we estimated by direct calculation its location based on isolated particles and their velocity. The real Bow shock is typically located at only 15 푅퐸 due to collective of solar wind plasma and accompanying phenomena.

The magnetopause is the abrupt boundary (“hard wall”) between a magnetosphere and the surrounding plasma. For , the magnetopause is the boundary between the planet's magnetic field and the solar wind. In the case of Earth, observed magnetopause is roughly at 10 푅퐸 . On quiet Sun’s days, one do not expect to observe many solar wind plasma particles for distances shorter than 10 푅퐸. Artistic representation of this phenomenon Projection onto noon–midnight meridian at a time near an equinox At a time near an equinox Earth’s rotation axis is perpendicular to the Earth–Sun line. The dipole axis will be tilted a bit, depending on the time of day. On the nightside the magnetic field is drawn out into a long tail consisting of two lobes separated by a 14 푅푒-thick sheet of particles called the . The plasma sheet (~2 million degrees) is about 10 times hotter than the solar wind. It has greater density (0.3 − 0.5 푖표푛푠/푐푚3) than lobes (0.01 − 0.02 푖표푛푠/푐푚3). The plasma sheet has an inner boundary about 11 푅푒 behind Earth. It also has upper and lower boundaries as shown on the previous slide. The projection of these boundaries onto the northern and southern portions of the atmosphere at about 67° magnetic latitude corresponds to two regions called the nightside auroral ovals. The aurora borealis and aurora australis (northern lights and southern lights) appear within the regions defined by the feet of these field lines and are caused by bombardment of the atmosphere by energetic charged particles. A video simulation of Earth's magnetic field interacting with the (solar) interplanetary magnetic field (IMF) Aurora The Aurora Borealis (Northern Lights) and Aurora Australis (Southern Lights) are the result of electrons colliding with the upper reaches of Earth’s atmosphere. (Protons cause faint and diffuse aurora, usually not easily visible to the human eye.) The electrons are energized through acceleration processes in the downwind tail (night side) of the magnetosphere and at lower altitudes along auroral field lines. The accelerated electrons follow the magnetic field of Earth down to the Polar Regions where they collide with oxygen and nitrogen atoms and molecules in Earth’s upper atmosphere. In these collisions, the electrons transfer their energy to the atmosphere thus exciting the atoms and molecules to higher energy states. When they relax back down to lower energy states, they release their energy in the form of light. This is similar to how neon light works. The aurora typically forms 80 to 500 km above Earth’s surface. On the dayside, magnetic field lines from high latitudes split, some crossing the Equator while others cross over the polar caps. The regions where the field lines split are called polar cusps. The projection of the polar cusps on the atmosphere at about 72° magnetic latitude creates the dayside auroral ovals.

Auroras can be seen in these regions in the dark hours of winter, but they are much weaker than on the nightside because the particles that produce them have much less energy.

The projections of the two lobes of the magnetic tail onto the atmosphere are the polar caps.

Before we discuss in more detail the Earth dipole field and Van Allen radiation belts let’s briefly touch upon Moon and Earth’s magnetic tail. Jack Schmitt, Apollo 17 mission, 1972 Earth’s magnetotail extends well beyond the of the moon and, once a month, the moon through it. This can have consequences ranging from lunar ‘dust storms’ to electrostatic discharges. The moon enters the magnetotail three days before it is full and takes about six days to cross and exit on the other side. During the crossing, the moon comes in contact with a plasma sheet. The lightest and most mobile of these hot charged particles, electrons, hit the moon’s surface and give the moon a negative charge. On the moon’s dayside this effect is counteracted to a degree by sunlight: UV photons knock electrons back off the surface, keeping the build-up of charge at relatively low levels. But on the nightside electrons accumulate and surface voltages can climb to hundreds or thousands of volts. The ground, meanwhile, might leap into the sky. There’s growing evidence that fine particles of moondust might actually float, ejected from the lunar surface by electrostatic repulsion. This could create a temporary nighttime atmosphere of dust and even diaphanous winds of particles flying from the strongly-negative nightside to the weakly- negative dayside.

Apollo never landed on a full moon and they never experienced the magnetotail. So this is yet just a hypothesis.

The “magnetic bottle” and Van Allen radiation belts

Magnetic bottle concept is used to confine (contain, trap) very hot plasma. The “magnetic donut” and Van Allen radiation belts

Because magnetic force do Particle velocity is more not do work, kinetic energy parallel to field lines in is almost constant. regions where lines are more parallel to themselves and more perpendicular to lines in regions where lines are converging .

Because Larmor radius increases as particles move further away from equatorial plane the particles spend more time in those regions near mirror points One feature on this is wrong. Which one? 푚푣 Recall Larmor radius 푅 = ⊥ with 푣 being component of velocity perpendicular to field. 푞퐵 ⊥

Near mirror points 퐵 is less than a factor 2 greater than near magnetic equatorial plane. However, 푣⊥ near mirror point is much, much greater than near magnetic equatorial plane. Why? 2 2 Since magnetic forces do not do work 푣 = 푣∥ + 푣⊥ ≈ 푐표푛푠푡. and near mirror point 푣∥ → 0 by

definition, hence 푣⊥ → 푣 . Therefore, Larmor radius is much greater near mirror points.

NO

Is this true? And if it is, what causes it? NO NEXT SLIDE Magnetic equatorial plane seen from southern (geographic) hemisphere

DRIFT OF ELECTRONS AND PROTONS Eastward drift Westward drift EARTH

B field stronger Lines denser

q < 0 q > 0

ELECTRONS PROTONS

B field weaker Lines sparser Mission of the first US (Explorer I)

Late in the evening of January 31, 1958, a 32-ton rocket blasted into space from Cape Canaveral, Florida, lofting the Explorer I spacecraft into orbit. It was a mission of firsts: Explorer I was the first U.S. satellite (joining , which had been launched the previous November by the Soviet Union).

The satellite carried a pioneering scientific payload (including Geiger-Muller tube counter), prepared at the State University of Iowa by a team of researchers led by James A. Van Allen. And the instruments on Explorer I made the first revolutionary discovery of the : Earth is enshrouded in doughnut-shaped rings, or toroid’s, of high-energy, high-intensity radiation.

High-speed particles from Van Allen belts can leak and collide with molecules in the atmosphere, giving rise to aurora displays. William Hayward Pickering, , and Wernher von Braun display a full-scale model of

A radiation belt is a layer of energetic charged particles that is held in place around a magnetized planet, such as the Earth, by the planet's magnetic field. The Earth has two such belts and sometimes others may be temporarily created.

The discovery of the belts is credited to James Van Allen, and as a result the Earth's belts are known as the Van Allen belts. Explorer 1 and confirmed the existence of the belt in early 1958 under James Van Allen at the University of Iowa. The trapped radiation was first mapped out by , and . Van Allen radiation belt

The main belts extend from an altitude of about 1,000 to 60,000 kilometers above the surface in which region radiation levels vary.

Most of the particles that form the belts are thought to come from solar wind and other particles by cosmic rays. The belts are located in the inner region of the Earth's magnetosphere. The belts contain energetic electrons and protons. Other nuclei, such as alpha particles, are less prevalent.

The belts endanger , which must protect their sensitive components with adequate shielding if they spend significant time in the radiation belts.

In 2013, NASA reported that the had discovered a transient, third radiation belt, which was observed for four weeks until it was destroyed by a powerful, interplanetary shock wave from the Sun.

Radiation belts exist around other and in the solar system that have magnetic fields powerful enough to sustain them. To date most of these radiation belts have been poorly mapped.

Van Allen radiation belt

It is generally understood that the inner and outer Van Allen belts result from different processes. The inner belt, consisting mainly of energetic protons, is the product of the decay of so-called "" which are themselves the result of cosmic ray collisions in the upper atmosphere. The outer belt consists mainly of electrons. They are injected from the geomagnetic tail following geomagnetic storms and are Cutaway drawing of two radiation belts around Earth: subsequently energized through wave- the inner belt (red) dominated by protons and the outer particle interactions. one (blue) by electrons. Image Credit: NASA The inner Van Allen Belt

The inner Van Allen Belt extends typically from an altitude of 600 mi (1,000 km) to 7,500 mi (12,000 km), i.e., 0.2푅퐸 − 2푅퐸 above the Earth. In certain cases when solar activity is stronger or in geographical areas such as the South Atlantic Anomaly (SAA), the inner boundary may go down to roughly 200 kilometers above the Earth's surface.

The inner belt contains high concentrations of electrons in the range of hundreds of keV and energetic protons with exceeding 100 MeV, trapped by the strong (relative to the outer belts) magnetic fields in the region. The inner Van Allen Belt

It is believed that proton energies exceeding 50 MeV in the lower belts at lower altitudes are the result of the of neutrons created by cosmic ray collisions with nuclei of the upper atmosphere.

The source of lower energy protons is believed to be proton diffusion due to changes in the magnetic field during geomagnetic storms.

Due to the slight offset of the belts from Earth's geometric center, the inner Van Allen belt makes its closest approach to the surface at the South Atlantic Anomaly (SAA).

The effect is caused by the non-concentricity of the Earth and its magnetic dipole. The SAA is the near-Earth region where the Earth's magnetic field is weakest relative to an idealized Earth-centered dipole field. Cosmic rays Cosmic rays are high-energy protons and atomic nuclei that move through space at nearly the speed of light. They originate from the sun, from outside of the solar system in our own galaxy, and from distant galaxies.

Generation of "albedo" neutrons beta decay Outside the nucleus, free neutrons are unstable and have a mean lifetime of 879.6±0.8 s. They decay to proton, electron, and electron antineutrino.

푝 휈ҧ 푒− 푒

Feynman diagram Also inside nucleus You might be asking: “How fast is 200 keV electron?” relativistic

Answer: 2.0845E+08 m/s or ~67% of speed of light 2 Rest mass frame energy E0 = 푚푐 or: “How fast is 100 MeV proton?” In frame moving with speed 푣 energy is E = 훾퐸0 where 훾 = 1 − 훽2 −1/2 with 훽 = 푣/푐. Kinetic energy is 퐾 = 퐸 − 퐸0 = 훾 − 1 퐸0 퐸 +퐾 퐸 Answer: 1.2848E+08 m/s or ~43% of speed of light Hence, 훾 = 0 = and 훽 = 1 − 훾−2 퐸0 퐸0

2휋 How long it takes for these particles to sweep say at 1푅 distance from surface of the Earth? 3 퐸 푚 (for particle with component of velocity parallel to field lines ~1.68 108 ≈ 56% 푐) 푠 2휋 2푅퐸 without twirling about filed lines only 3 ~0.16 푠 푣∥ . but with twirling included it could take much longer Electron fluxes in the outer Van Allen belt (left) and proton fluxes in the inner belt (right) are projected in a “spirograph” pattern over the northern pole of the Earth. The projections show the bands of particle energies within each belt. The gap shown in the inner belt at the magnetic field distortion feature is a result of the tipped magnetic pole of the Earth. The outer Van Allen Belt

The outer belt consists mainly of high energy (0.1–10 MeV) electrons trapped by the Earth's magnetosphere. It is almost toroidal in shape, extending 3-10 Earth radii (푅퐸) from the center of the Earth. Its greatest intensity is usually around 4–5 푅퐸.

The outer electron radiation belt is mostly produced by the inward radial diffusion and local acceleration due to transfer of energy from whistler-mode plasma waves to radiation belt electrons.

Radiation belt electrons are also constantly removed by collisions with atmospheric neutrals, losses to magnetopause, and the outward radial diffusion. The outer Van Allen Belt

In 2014 it was discovered that the inner edge of the outer belt is characterized by a very sharp edge, below which highly relativistic electrons (> 5MeV) cannot penetrate. The reason for this shield-like behavior is not well understood.

The trapped particle population of the outer belt is varied, containing electrons and various ions. Most of the ions are in the form of energetic protons, but a certain percentage are alpha particles and O+ oxygen ions, similar to those in the ionosphere but much more energetic. This mixture of ions suggests that particles probably come from more than one source.

The outer belt is larger than the inner belt and its particle population fluctuates widely. Energetic (radiation) particle fluxes can increase and decrease dramatically as a consequence of geomagnetic storms, which are themselves triggered by magnetic field and plasma disturbances produced by the Sun. The increases are due to storm-related injections and acceleration of particles from the tail of the magnetosphere. Solar storm concerns If there is a major magnetic eruption on the Sun, the resulting outrush of particles may break through the outer magnetosphere and overload the Van Allen belts in more destructive ways. The rapid injection of particles into the belts can damage the circuitry and solar panels on satellites in orbit; swarms of protons and electrons released when solar wind particles crash into the atmosphere induce electrical currents that can overload terrestrial power systems and cause blackouts.

Almost exactly a century preceding the Explorer I launch, on the night of August 28 to 29, 1859, people around the world got to witness what happens when an enormous solar storm overwhelms Earth’s magnetosphere. The New York Times reported that thousands of New Yorkers watched “the heavens…arrayed in a drapery more gorgeous than they have been for years.” An even more spectacular aurora display occurred on September 2, when the sky lit up as far south as Central America in the Northern Hemisphere. Disturbances in Earth’s magnetic field were so powerful that magnetometer readings were driven off their scales. Telegraph networks were unusable for nearly eight hours in most parts of the world due to high-energy particles in the atmosphere. In several regions, operators reported that their telegraphs were sparking from the electrical current induced by the aurora. In 1989, just before the rise of the Internet and GPS systems, a smaller but still potent solar storm demonstrated the heightened risk. The 1989 storm induced huge ground currents that knocked out Quebec’s electrical power grid and caused problems at 200 sites in the United States. Implications for space travel

A region between the inner and outer Van Allen belts is sometimes referred to as the "safe zone". Solar cells, integrated circuits, and sensors can be damaged by radiation. Geomagnetic storms occasionally damage electronic components on spacecraft.

Miniaturization and digitization of and logic circuits have made satellites more vulnerable to radiation, as the total in these circuits is now small enough so as to be comparable with the charge of incoming ions. Electronics on satellites must be hardened against radiation to operate reliably.

Some satellites have its sensitive electronics components turned off when passing through regions of intense radiation.

A satellite shielded by 3 mm of aluminum in an elliptic orbit 320 by 32,000 km passing the radiation belts will receive about 2,500 rem (25 Sv) per year (for comparison, a full-body dose of 5 Sv is deadly). Almost all radiation will be received while passing the inner belt. Radiation dose according to EPA https://www.epa.gov/radiation/radiation-terms-and-units

Absorbed dose describes the amount of radiation absorbed by an object or person. The unit for is the (Gy, international unit) or the (U.S. unit). One gray is equal to 100 rads.

​Effective dose describes the amount of radiation absorbed by person, adjusted to account for the type of radiation received and the effect on particular organs. The unit used for effective dose is (Sv, international unit) or rem (U.S. unit). One Sievert is equal to 100 rems. Implications for space travel

The Apollo missions marked the first event where humans traveled through the Van Allen belts, which was one of several radiation hazards known by mission planners. The astronauts had low exposure in the Van Allen belts due to the short period of time spent flying through them. Apollo flight trajectories bypassed the inner belts completely to send spacecraft through only the thinner areas of the outer belts.

Astronauts' overall exposure was actually dominated by solar particles once outside Earth's magnetic field. The total radiation received by the astronauts varied from mission to mission but was measured to be between 0.16 and 1.14 rads (1.6 and 11.4 mGy), much less than the standard of 5 rem (50 mSv) per year set by the United States Atomic Energy Commission for people who work with radioactivity. Cosmic microwave

The cosmic microwave background (CMB) radiation (CMBR) is electromagnetic radiation which is a remnant from an early stage of the universe, when neutral atoms first formed and photons decoupled from initial plasma, also known as "relic radiation". The photons that existed at the time of photon decoupling (T~3,000K) have been propagating A map of the Universe’s cosmic microwave background ever since, though growing fainter and less energetic, since the radiation, and its polarization, measured by the Planck satellite. expansion of space caused their wavelength to increase over time. Temperature fluctuations amount to about one part in 100,000—not much higher than the measurement accuracy. The CMBR studies helped pin the age of Universe to about 13.8 billion years.

The CMBR is faint cosmic background radiation filling all space. It is 2.72548±0.00057 K almost isotropic, that is not associated with any star, galaxy, or other object. This glow is strongest in the microwave region of the radio spectrum. The accidental discovery of the CMB in 1965 by American radio astronomers Arno Penzias and Robert Wilson was the culmination of work initiated in the 1940s and earned the discoverers the 1978 Nobel Prize in Physics. A few interesting, medium duration, videos https://www.youtube.com/watch?v=DGzL3dodGC4

Magnetism - Defending Our Planet, Defining The Cosmos (23 min 32 sec) NASA Multimedia Science MAGNETISM is a full dome planetarium show that demonstrates how the Earth’s magnetic field protects our planet from energetic particles from the Sun and galaxy, and how the magnetic field also protects the water in our atmosphere from being swept away by the solar wind. It shows the first aurora seen simultaneously from the ground and from the ISS, and tells about the MMS mission (Magnetospheric Multiscale) and its quest to understand the magnetic connection between the Earth and the Sun. https://www.youtube.com/watch?v=QiheGigtnws

What's Wrong with Earth's Magnetic Field? (14 min 37 sec) Curious Droid Strange things are happening in space but the cause is right below our feet. The earth's core is changing and the magnetic poles could possibly flip in the not too distant future. We are just discovering a whole new hidden weather system in the earth molten core that has direct effects on the magnetic field which in turn will have a major effect on our future technological development. But all is not lost, we can work our way out of this but time is of the essence because we don't know just when things are going to get tricky