Muon Cts/min Vs Altitude(ft)

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Victor Hess
Before making balloon ascents himself, he determined the
height at which ground radiation would stop producing
ionization (about 500 meters) and designed instruments that
would not be damaged by temperatures and pressure
changes. He then made ten ascents (five at night) - two in
1911, seven in 1912, and one in 1913 - and found that
ionization soon ceased to fall off with height and began to
increase rapidly, so that at a height of several miles it was
many times greater than at the earth's surface. He
concluded, therefore, that "a radiation of very high
penetrating power enters our atmosphere from above."
On one ascent, during an almost total eclipse of the sun, the
radiation was not diminished. Hess therefore concluded that
the rays could not be emitted by the sun.
Hess was awarded the Nobel Prize in 1936 for this work
(along with the discoverer of the Muon, Anderson).
PARTICLES!
NUMBER
Primary Cosmic “Rays”
Largely protons (H, hydrogen nucleus)
Energies peak ~ 300 MeV (0.3 GeV)
Come from all directions
From the galaxy, not the sun so much
~ 5000 particles /meter2/second
Only the faster ones make “good” muons
~500 protons/meter2/second
ENERGY
1 eV
1 KeV
1000
e
1 MeV
million
1 GeV
billion
p Most Powerful Accelerator
mp p a
Charging Snail
Fast-ish Cosmic “Rays”
Gamma Rays
e in TV picture tube CRT
Ionize Atom
Visible Light Photon
Energy & eV, MeV, GeV stuff
Mass energy
1 TeV
trillion
Cosmic Ray Essentials
p (cosmic “ray”)
Encounters air
N or O nucleus
around 15 km altitude
pion
produced
p
stuff
m
other stuff
pion
decays into muon
e
e
e
e
Gently slows down knocking off
many (~million) air molecule’s
electrons
e
Muon may hit your sensor
unless decays first
Muons /cm2/sec
Muon Flux at Surface
(above some Energy)
0.01
Less than
1 per minute
In a square
centimeter
Muon Energy (GeV)
Relative Number
# Muons Change with Angle
Angle off Vertical
Muon Rate vs Altitude(ft)
Ct/min
Feet
Count Rate Increases ~ 100% over 10000 ft.
So IF a straight line – expect 10 % increase in 1000 ft
How can
this be?
~ 30% Difference
from close locations
Muon Counting Headaches
due to Statistics
What is your best estimate of the average
result if you did it a zillion times?
How confident are you with the estimate?
EXAMPLE:
Count random “hits” over 30 seconds,
multiple times - when the TRUE average
rate is 1 per second.
One 30 Second Trial
Another 30 Second Trial
10X 30 Second Trials
Average -> TRUE with Trials
40
HitsIn30sec
HitsIn30
AveafterTrials
35
TRUE
30
25
20
15
0
2
4
6
30 sec Trail#
8
10
12
Uncertainty Reduced with Trials
HitsIn30sec
45
Best Estimate of Average # Hits
in 30 sec and an estimate
of Uncertainty after 300 sec
40
35
30
25
20
15
0
2
4
6
8
30 sec Trail# (accumulated)
10
12
Distribution for 1000 Trials
1000 Trials Distibution
# of Times from 1000
100
80
60
40
Average 30.03
stdev=5.02
20
0
1
9
17 25 33 41 49 57 65 73 81 89 97
Hits in 30 Sec
Is Result More for Test 1 or Test 2?
10
8
6
4
2
0
0
1
2
3
0
1
2
3
0
1
2
3
10
8
6
4
2
0
10
8
6
4
2
0
A Note of Caution from
Professor Hess
… discovered that up to about 700
meters the ionization rate
decreased but then increased with
altitude …
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