Carl Størmer
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as it arrives from infinity and interacts with the dipole. | as it arrives from infinity and interacts with the dipole. | ||
Intuitively it is clear that a particle with a sufficiently high rigidity will | Intuitively it is clear that a particle with a sufficiently high rigidity will | ||
- | penetrate the dipole field and precipitate the Earth. | + | penetrate the dipole field and "precipitate" onto the Earth somewhere. |
- | The minimum such rigidity is called the "cutoff rigidity" and, not so | + | The minimum such rigidity at a given geographic point is called the "cutoff rigidity" and, not so |
- | intuitively, the mapping of greater rigidities at | + | intuitively, the mapping of greater rigidities at this terrestrial point onto |
the celestial sphere is not simple - the point becomes | the celestial sphere is not simple - the point becomes | ||
a line parametrized by rigidity. | a line parametrized by rigidity. | ||
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geophysical matters, such as atmospheric pressure fluctuations. | geophysical matters, such as atmospheric pressure fluctuations. | ||
- | [[File:429f2.png|600px|thumb|center|<b>Figure | + | [[File:429f2.png|600px|thumb|center|<b>Figure 2:</b> |
Map of cutoff rigidities, ranging up to more than 16 GV. | Map of cutoff rigidities, ranging up to more than 16 GV. | ||
The neutron monitor at Doi Inthanon, Thailand, is in the highest contour | The neutron monitor at Doi Inthanon, Thailand, is in the highest contour | ||
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[[File:429f3.png|400px|thumb|center|<b>Figure 3:</b> | [[File:429f3.png|400px|thumb|center|<b>Figure 3:</b> | ||
- | + | Størmer's sketch of a forbidden zone, showing the characteristic mirroring | |
- | motions of a particle that cannot escape; in | + | motions of a particle that cannot escape; in 3D this zone becomes a torus |
("belt") surrounding the Earth and in the | ("belt") surrounding the Earth and in the | ||
[https://en.wikipedia.org/wiki/Adiabatic_invariant adiabatic limit] | [https://en.wikipedia.org/wiki/Adiabatic_invariant adiabatic limit] | ||
indeed particles are trapped in these belts. | indeed particles are trapped in these belts. | ||
]] | ]] | ||
+ | |||
+ | This figure would also serve perfectly well to illustrate the trapping of energetic | ||
+ | particles in flare loops, a bit of physics frequently mentioned in RHESSI Nuggets. | ||
+ | Here the trapping has limits because of the lack of cylindrical symmetry in the | ||
+ | magnetism of a solar active region, and the consequent interruption of the | ||
+ | [https://en.wikipedia.org/wiki/Adiabatic_invariant third adiabatic invariant]. | ||
== Conclusion == | == Conclusion == |
Latest revision as of 19:44, 29 May 2022
Nugget | |
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Number: | 429 |
1st Author: | Hugh HUDSON |
2nd Author: | Lyndsay FLETCHER |
Published: | 15 April 2022 |
Next Nugget: | TBD |
Previous Nugget: | Solar Hard X-rays with Insight |
List all |
Contents |
Introduction
Carl Størmer (1874-1957) followed Kristian Birkeland (subject of an earlier Nugget) in the illustrious history of Norwegian pioneers of space weather. Both were active during the early years of 20th century Oslo. Figure 1 is a well-known picture showingf Størmer engaged in photographing the aurora (with a Birkeland, but not the famous one, taking notes). This photography led to triangulation that demonstrated the high altitude of the auroral phenomenon, thus eliminating terrestrial explanations. The mystery here is that this famous photograph seems to have been taken in broad daylight, certainly not the best time to see the aurora.
The origins of cosmic rays
Størmer solved the difficult mathematical problem of defining the trajectory of a charged particle in a dipole magnetic field. His hope was to be able to trace cosmic rays, as observed at the Earth's surface, back to their celestial origins. This is just the numerical integration of the Lorentz force on a particle of specified energy (or rigidity) as it arrives from infinity and interacts with the dipole. Intuitively it is clear that a particle with a sufficiently high rigidity will penetrate the dipole field and "precipitate" onto the Earth somewhere. The minimum such rigidity at a given geographic point is called the "cutoff rigidity" and, not so intuitively, the mapping of greater rigidities at this terrestrial point onto the celestial sphere is not simple - the point becomes a line parametrized by rigidity. Modern calculations give results such as those in Figure 1 here, and are routinely important for interpreting "cosmic ray" variations via neutron monitors in a network across the Earth. Almost all of the variability comes not from the true cosmic rays, which interested Størmer as an astronomer, but from solar particles and geophysical matters, such as atmospheric pressure fluctuations.
Størmer's Calculations
The actual calculations (Ref. [1] and elsewhere) can only be described as mathematically horrific. Because most of the computational work was done by hand, Størmer devoted great effort mathematically to re-casting the differential equations into forms that lent themselves to basically manual numerical work. Nevertheless, he and his helpers solved the problem for the idealized dipole; nowadays it is solved repeatedly for realistic geomagnetic and interplanetary magnetic fields, allowing for their time variations. As a byproduct, he anticipated the later discovery of the Van Allen Belts (see Ref. [2] for a full historical account as of 1968). Figure 3 reproduces a Størmer graphic showing one of his "forbidden zones" - extraterrestrial cosmic rays cannot get into these volumes, but conversely they form (ideally) permanent traps for particles. In hindsight, one might have known that these horrible calculations led to an extremely interesting prediction.
![](/~tohban/wiki/images/thumb/c/c0/429f3.png/400px-429f3.png)
This figure would also serve perfectly well to illustrate the trapping of energetic particles in flare loops, a bit of physics frequently mentioned in RHESSI Nuggets. Here the trapping has limits because of the lack of cylindrical symmetry in the magnetism of a solar active region, and the consequent interruption of the third adiabatic invariant.
Conclusion
This probably concludes our series of RHESSI Nuggets on Norwegian pioneers of heliophysics, although there are Rosseland and others to think about. We've only touched on one of Størmer's contributions, but it was a fundamental one.
References
[1] "On the Trajectories of Electric Particles..."
[2] "Space Radiation", by W.R. Corliss
RHESSI Nugget Date | 15 April 2022 + |
RHESSI Nugget First Author | Hugh HUDSON + |
RHESSI Nugget Index | 429 + |
RHESSI Nugget Second Author | Lyndsay FLETCHER + |