IMSR07: Radiation Belt contributions from the Heliospheric “Cusps”

Robert Sheldon

June 27, 2005

National Space Science & Technology Center

Outline

I. Define GCR, ACR

II. Define Quadrupole advantage

III. Apply Quadrupole theory to the

generation of ACR & GCR

Cosmic Rays

• Cosmic rays are >MeV particles creating air showers as they impact the Earth’s atmosphere.

• They are subdivided into 3 categories: Galactic, Anomalous, and Solar, presumably on their origin.

• All of the hazards of radiation belt particles apply to these particles, only they are generally not as intense.

• GCR prediction is easy, it is constant

• ACR is slowly varying with solar cycle

Anomalous Cosmic Rays• Singly-ionized, lower in energy than GCR• Thought to be neutral Local Interstellar Medium

atoms that :– penetrate the heliosphere, – photoionize around 5 AU (for H&O, 1 AU for He), – are picked up by solar wind ~ 2keV/nuc– Fermi-accelerated between shock & heliopause– Diffuse back toward the Earth

• Some problems:– Diffusion theory gives the wrong solar-cycle prediction– Fermi-accel has too many adjustable parameters

Prediction of GCR, ACR

• The acceleration of GCR has been mysterious since their discovery. Fermi developed two theories of GCR acceleration which today are generally applied to supernovae (SN).

• The acceleration of ACR has a well-determined location at the heliopause, but the method of acceleration is still somewhat mysterious.

• Without a well-understood theory of acceleration, there can’t be a good prediction either.

Why Quadrupoles are a superior accelerator for Cosmic Rays

• Accelerator efficiency is a chain of many factors: source rates, power available, conversion efficiency, extraction efficiency, etc. Thus it is a product of all these others.

T = 1 2 3 4 5 6 7…• We compare the three near-Earth traps that are

known to accelerate particles, estimating their individual efficiencies:– Fermi (1-D compression parallel to B, upstream events)– Dipole (2-D compression perp to B, rad belts)– Quadrupole (2-D compression perp to B, cusp particles)

PROPERTY DIPOLE FERMI QUADRUPOLE

Stochasticity .001:1:1000 s .001:>103:>104 s 0.1:1:10 s

Process Flow rim>ctr>blocked end>side>diffus ctr>rim>open

Wave Coupling hi E weak all E same hi E best

Accel. in trap Traps Detraps Trap/Release

Diffusion Essential Helpful Neutral

Adiabatic Heat 2D pancake 1D cigar 2D pancake

Energy Source SW compress SW Alfven SW+internal

e- Max Energy 900MeV@10Re 1.8 MeV@.1Re 280 MeV@3Re

e- Min Energy 45 keV 2.5 keV 30 keV

Trap Volume 1024 m3 1020 m3 1022 m3

Trap Lifetime >1013s 104s 109:105s

Accel. Time >300,000s 8,000s 25,000s

Trap Power <5x108W 106W 5x107W

Cosmic Ray Efficiency: Quadrupole vs Dipole Traps

• Magnetic gradients permit trapping:– Dipole is a negative gradient with r– Quadrupole is a positive gradient with r– Current wires are negative gradient with z– Neutral sheets are positive gradients with z

• A particle escaping the trap is adiabatically affected:– Dipole & currents cool– Quadrupole & neutral sheets heat

• Source injections are external for dipole & current sheet, internal for Quadrupole & neutral sheet

Cosmic Ray Efficiency: Quadrupole vs ‘Monopole’ Traps

• No, there are no magnetic monopoles, but a Fermi-trap is 1-D, whereas neutral sheets are 2D, and dipole/quadrupole are 2.5D.

• Fermi-traps have lower efficiency than 2D traps– Acceleration is parallel to B, and detraps as it accelerates.

Models have to incorporate some internal scattering to keep it efficient

– “mirrors” on the ends of the trap are very leaky. Models generally use flat-plane geometries with best reflection.

– Upstream mirror is thought to be turbulence, which may have a feedback, but is an adjustable parameter in model

Heliospheric Neutral Sheets

• The Sun’s dipole is tilted to its spin axis. So from Earth perspective, we have 13 days of Bz North, 13 days of Bz South, about 3AU wide. These reversals of B-field are separated by a neutral sheet.

• Between the termination shock & the heliopause, this magnetic striping compresses to 1AU strips of approx. 0.2nT

Trapping in neutral sheets

We know that higher energies have larger gyroradii, which are only trapped if they fit inside a layer. So we calculate maximum energy that fits:

p= qB

= [1 + (p/mc)2 ]1/2

K = ( –1)mc2 ([1 + (qB/mc)2 ]1/2 –1)mc2

Therefore we can calculate the cutoff K, for a given (q,,B).

ACR Theory

Data

MeV/nuc

~3000

~400

~400

~60

~15

ACR Predictions

• If this be the mechanism that generates ACR, then the prediction will depend on the Vsw, Bsw and the degree of tilt of the magnetic dipole on the Sun. Since this solar observation takes ~1yr to reach the heliopause, the prediction is equally long.

• While not helping commercial satellite customers, such a 1-yr prediction would be important for manned missions.

Low energy nuclei

composition

GCR Spectra

Properties of GCR• Energy density of GCR = 1 eV/cc (~6 @ galact. ctr)

• Energy density of Interstellar Medium components:

• GCR have equivalent energy to all other ISM stuff.

Are GCR from Supernovae?• Power output of Supernovae shock ~1051/30yr = 1035W, of

which and estimated 15% show up in GCR, or 2e34 Watts.• Lifetime of GCR ~ 1015s. (from 10B spallation)• Energy Density * Volume /Time = 1eV/cc*1069cc/1015s = 3x1035Watts (and it only gets worse if you use the numbers

in the galactic center) giving a ratio: SN/GCR = 0.1 !Another calculation: Energy Density * velocity * area =

luminosity 1eV/cc * 3e10cm/s *5e45cm2 = 1e35 Watts• Even if the entire energy of a supernova went into GCR, and

as we argued earlier, acceleration is a very inefficient process, we would still have an energy budget problem!

• (As some wag put it, SN are already highly oversubscribed, everyone already invokes it for their energy source)

• Where is the energy for GCR coming from?

Some more peculiar coincidences• Energy density of starlight = 0.3 eV/cc

• Energy density of ISM = ~1 eV/cc

• Energy density of interstellar B-fields = 0.2 ev/cc

• Cosmic Background Radiation = 0.3 eV/cc

• Nuclei 98%, electrons 2%

• Everyone calls these “coincidences”, but perhaps there is a theory that links them all together. My contention is that quadrupole cusp acceleration is just such a proto-theory.

Quadrupole Cusps Pressure Balance• Dimensional analysis: Energy/Vol Force/Area =

Pressure. Thus mechanisms that equalize pressure will also equalize energy density.

• In a galaxy with a dipole magnetic field embedded in a flowing plasma, the cusp topology (and strength of the magnetic field) is affected by the ram pressure. Thus we can write an equilibrium:

PGCR + Pmag + Pstarlight = Pram_H + PCMB

• Assuming that equipartition has balanced the IGM Pram_H = PCMB

• Thus we explain all these “coincidences” as a pressure equilibrium in the quadrupole cusp

Energy Sources for GCR• Where does the energy come from? Supernovae of

course! Seriously, shock waves travelling out of the galactic disk transmit energy to the cusp & compress it, just as much as turbulence in the intergalactic medium (IGM). The cusp is a low-Q object, energy (waves) goes in, and doesn’t come out.

• The advantage over Fermi-acceleration at SN? Continuous acceleration, multiple energy sources, identifiable rigidity properties. And the clincher…

• A natural explanation of the “knee”. At low-E, protons have the smaller rigidity, at high E, (due to gamma) Fe has the smaller rigidity. So they cross.

GCR predictions

• If this is the energy source for GCR, then galactic disturbances propagate to the trap, and accelerate particles that then fill the galaxy. SN are a candidate

• With 10-100k ly distances in the galaxy, these are predictions we may never be able to test.

• However, astronomical observations of historical SN may fit historical trends in 14C data.

Conclusions

• Although most cosmic rays are transient visitors in the radiation belts, they are still of concern to satellites and humans in space.

• Our application of quadrupole traps to cosmic ray generation may explain a number of mysteries about their origins.

• More significantly, it provides predictions for both populations: one year predictions for ACR, and 100kyr for GCR. These can be tested for historical accuracy from 14C, for example.