The origin of all cosmic rays : a space-filling mechanism. Page: 4 of 8
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ORIGIN OF COSMIC RAYS
3) The evidence for acceleration due to quasi-parallel heliosphere shocks from
satellite measurements near the earth is weak, in some cases with small or no
evidence for the expected strong hydromagnetic turbulence, and where
acceleration is demonstrated only after a few shock traversals by the accelerated
particles. Thus no more than 10 kT acceleration has been observed whereas
1020 kT must be achieved.
4) Laboratory experiments necessary to demonstrate shock acceleration have not
yet succeeded and space observations have failed to observe the necessary
turbulence of the collisionless shock.
5) The argument that a unique power-law spectra resulting from shock
acceleration is not compelling.
6) The above argument of number of scatterings per shock crossing and a non-
linear wave amplitude of B/delta B - 10, implies a shock thickness of
n RLarmor = 10 (c/vshock) RLarmor = 1 kpc at 1015 ev, the "knee" of the
spectrum, and therefore a thickness significantly greater than the thickness of the
galaxy.
3. Power-law Spectrum
The accepted theory of cosmic ray acceleration is shock wave
acceleration in the ISM driven by supernova (Axford, Leer, and Skadron, 1977;
Bell, 1978; Blanford and Ostriker, 1988). "This acceptance has been largely
based upon the good agreement between the "universal" power-law spectrum
predicted by shock acceleration i.e., the power-law index becomes:
s=(d lnN)/(d In E) -(2+e)
depending only on the Mach number and the observed or inferred particle
spectra." (see Blanford and Eichler, 1987 for a review, and many papers by P.
Biermann for a more accurate comparison.) This belief that a nearly correct
power-law spectral index alone is unique is instead, a less restrictive condition
than commonly believed. Any accelerator for which a fractional gain in energy,
(d In E), by a few particles is accompanied by a fractional loss, -(d InN), in
number of the remainder will give a power-law:
dN/N = -s(dE/E).
The fractional loss for a fractional gain in energy is what would be expected for a
rigidity dependent loss mechanism where the probability of a relativistic particle
being scattered out of an acceleration region is inversely proportional to its
energy or rigidity.
For values of s <-2, i.e. a smaller fractional loss, the integral energy
E
becomes asymptotically large, f NdE wES-2 and at some energy will truncate
03
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Colgate, S. A. (Stirling A.) & Li, H. (Hui). The origin of all cosmic rays : a space-filling mechanism., article, January 1, 2001; United States. (https://digital.library.unt.edu/ark:/67531/metadc927481/m1/4/: accessed April 24, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.