How to calculate speed of cosmic ray particles from kinetic energy

28 11 2011

In high energy and astroparticle physics energies for cosmic ray particles are given in GeV/n. But how much is that in term of speed?

First of all we must remember that these energies are kinetic energies (k).

The total energy E of a particle is the sum of its kinetic energy k and its mass m: E = m + k with c=1 and energy and mass measured with the same unit.

In special relativity: E = g m where g is the Lorentz factor that is equal to:

\gamma \equiv \frac{c}{\sqrt{c^2 - v^2}} = \frac{1}{\sqrt{1 - \beta^2}} = \frac{\mathrm{d}t}{\mathrm{d}\tau}


\beta = \frac{v}{c}

is the ratio between the speed of a particle and the speed of light c.

Remember that the mass of a proton is m=0.938 GeV. Lorentz factor is then given by: image or image and b is then image

Assuming that mass is linear with number of nucleons in the nucleus, the same calculation applies to any ion using the kinetic energy per nucleon. We see that for energies bigger than 2 GeV/n particles travel almost at light speed (> 95 %).

k g b
100 KeV 1.000107 0.0146
1 MeV 1.001066 0.04614
10 MeV 1.010661 0.14486
100 MeV 1.106610 0.42825
1 GeV 2.066098 0.87507
2 GeV 3.132196 0.94767
5 GeV 6.330490 0.98744
10 GeV 11.66098 0.99632
100 GeV 107.6098 0.99996


This post was inspired by Protoni quasi veloci come la luce and Protoni quasi veloci come la luce: soluzione


Short digression on particle energy

28 11 2011

The units used to measure energy in everyday life, like the Joule or the Calorie, are not well suited to elementary particles with very small such as protons or electrons, or nuclei of cosmic rays.

In this case particle physicists measure the energy in terms of electronVolt (eV). 1 eV is the energy acquired by a free electron when accelerated by an electrical potential difference of 1 Volt in vacuum. To make an example, a free electron placed in a field generated by a 12V battery would be accelerated by the potential difference and would acquire an energy of 12 eV. To convert eV to Joule we must recall that electrical potential is calculated dividing potential energy by electrical charge. So multiplying the electron charge by one Volt will do the job:

1 eV = e * 1V = 1.6 * 10-19 C * 1 V = 1.6 * 10-19 J

This is a very low energy. Electrons and protons in the hot solar corona, where temperature is about 1 million degree, have a mean energy of 100 eV. But as we already saw here, cosmic rays have much higher energies. To be detectable on ground, for example, cosmic rays impinging on Earth atmosphere must have a minimum energy of 450 MeV (450 millions eV).

To know how particle energy is related to its speed, stay tuned. I will talk about it in a future post: How to calculate speed of cosmic ray particles from kinetic energy.

Galactic cosmic rays (GCR)

27 11 2011

We already gave a general look at the various components of the cosmic rays in Earth orbit. Now let’s look closer at them. We start from the galactic cosmic rays (GCR).

GCR originates within our Galaxy and they are accelerated by supernovae explosions. The higher energy component comes from outside the galaxy and its acceleration mechanism is still not clear.

We already showed that cosmic ray energies range from 10 MeV up to 1012 MeV. Obviously, the particle flux varies with the kinetic energy as it is shown in the following figure.

Cosmic ray flux versus particle energy

It’s worth noting that for energies less than 1010 eV (that is 104 MeV or 10 GeV) the flux is 1 particle per second per square meter, at 1015 eV (around the knee region) the flux is 1 particle per year per square meter and at higher energies the flux is about 1 particle per year per square kilometer.

At these energies the cosmic rays are essentially made by protons. The heavier the nuclei the lower the flux (apart from the odd/even effect). In the following figure we can compare fluxes of protons, alpha particles (helium nuclei), electrons, Carbon nuclei and Iron nuclei.


To understand the energy magnitude we are talking about and the effects of energetic particles I want to talk about a very interesting phenomenon (without entering details): the Extensive Air Shower. A particle entering the atmosphere meets with an increasing number of nuclei and molecules, mainly Nitrogen and Oxygen. Sooner or later the cosmic ray will collide with one of them. This interaction could originate secondary particles by converting its kinetic energy into mass according to the famous formula

E = mc2

One single particle with kinetic energy of 10 EeV (that is 1019 eV) entering the atmosphere originates up to 100 billions particles at sea level over an area of some square kilometers as shown in this simulation


These ultra high energy cosmic rays are studied by ground based stations as the Auger observatory in Argentina. They are composed by a group of detectors that measure both the atmospheric fluorescence due to particle showers and the particles that reach the ground. Fluorescence telescopes measures ultraviolet light produced by the shower and they are so sensitive that can detect a shower 15 km far. Ground detectors are 1600 water tanks, each filled with 12000 liters, and far 15 km from each other. They detect Cherenkov light that is produced by particles that travel faster than light in water (Cherenkov light principle is similar to sonic boom one).


And all is distributed over an area of more than 10 squares miles…


These ultra energetic particles have an extragalactic origin (because galactic magnetic field is not strong enough to contain them) and in 2007 the scientists of the Auger Collaboration announced that AGN (Active Galactic Nuclei) are the most probable sources of this kind of cosmic rays.

This post is a little off topic for this blog, but I consider these ultra energetic cosmic rays so interesting… In the near future I will talk about less extreme energies that are more related to ALTEA and its research on the International Space Station

For further details:

Auger Observatory closes in on long standing mystery, links highest-energy cosmic rays with violent black holes

Meet the first explorers of Mars

22 11 2011

After a 520 day trip, on November 4th 2011, the six explorers that walked on Mars for the first time came back on planet Earth. They went out from the hatch of their spaceship and they were welcomed by many scientist that run to Moscow for this event. They will visit Rome on December 6th during their world tour, and I will be there to meet two of them.

How is it possible that Russia sends a spaceship to Mars and none is talking about it?

We are talking about Mars 500 mission, that started June 3rd 2010 (yes, you read it right, 2010). Mars 500 is the first full-time simulation of a trip to Mars, during which six volunteers lived for more than 520 days in a laboratory placed in the Institute of Biomedical Problems (IBMP) of Moscow. The lab simulates both the spaceship and the surface of Mars.

On the 6th of December ESA is organizing the Mars 500 Space Tweetup in Rome. For this event ESA selected 20 people to meet two members of Mars 500 crew, Diego Urbina (@diegou) and Romain Charles (@Romain_Charles). And I was lucky enough to be among these 20. The live tweeting of this event will use #mars500tweetup hashtag. So follow me on twitter (@luke2375) on the 6th of December.

If you want to address any question to Diego Urbina or Romain Charles, please leave a comment. You will find the answers to the best questions on this blog.

Space Radiation in Earth Orbit

15 11 2011

The Light Flash phenomenon is only one effect that is caused by cosmic rays in Earth Orbit or in the Solar System. Our planet with its atmosphere and its magnetic field shields us from cosmic rays and their dangerous effects.

Earth magnetic field offers a partial protection from cosmic radiation to astronauts in Low Earth Orbit (LEO) during Shuttle or ISS missions, while exiting the magnetosphere (missions to the Moon or to Mars) would expose astronauts to higher radiation doses. Anyway during all space missions, even LEO ones, ionizing radiation levels are higher than on Earth surface.

The main radiation sources in LEO are galactic cosmic rays, solar particles and particles trapped in the Van Allen belts.

Galactic cosmic rays (GCR) are charged particles, mainly nuclei:


Nuclei are mainly composed by protons (87%) and helium (12%), while heavy nuclei are mostly carbon, nitrogen and oxygen nuclei. Heavier nuclei up to uranium are present in smaller quantities

Cosmic rays kinetic energies range from some MeVs up to 1012 MeV (who does not like powers of ten would like to know that 1012 is equal to ten with twelve zeroes, that is For energies higher than 2 GeV for nucleon (that is 2000 MeV for nucleon) these particles travel at speed near to speed of light: they come from our galaxy after being accelerated by supernovae explosions; particles of higher kinetic energy are of extragalactic origin and their acceleration mechanism is still under debate.

Solar particles compose the solar wind and are mainly composed by low energy protons and electrons (kinetic energy less than 100 MeV) coming from outer shells of the Sun (the chromosphere) at speed around 400 km/s. Usually solar particle are not of great hazard, but particle events associated with solar flares of coronal mass ejections could occasionally cause a sudden increase of particle flux with possible risks for astronauts safety.


Solar flare of 13 February 2011. Credit: NASA/SDO

These two components can be found even outside earth magnetosphere and must be taken into account when planning missions outside Earth orbit.

The third radiation component can be found only in Earth orbit. Charged particles are trapped by the magnetic field in the radiation belts (Van Allen belts): the inner belt is mainly composed by protons and the outer one is composed by electrons. The outer belt is crossed by geostationary satellite orbits used for telecommunications. Solar storms cause an increase of particle flux and could harm or damage these satellites. The inner belt is crossed by the orbit of the Space Shuttle of the space stations.

Near the Earth the cosmic rays are almost totally deflected by the magnetic field that acts as a shield. These particles could be channeled along the field lines near the poles originating the fascinating effect known as aurora. These auroras are visible also on other planets.


The orbit used for long term missions is the result of a compromise between a stable orbit (out of the atmosphere to avoid friction) and a safe environment for the astronauts (far away from the center of the inner radiation belt).

Previous posts:
Cosmic rays and human exploration of space
ALTEA- An Italian experiment onboard the International Space Station
The effects of cosmic rays on astronauts: the Light Flash phenomenon

Further readings and sources:
Raggi cosmici e missioni spaziali (in Italian)
A special thanks to Riccardo ‘Unreal’ Rossi for pictures suggestions (via Facebook)

The effects of cosmic rays on astronauts: the Light Flash phenomenon

1 11 2011

Cosmic rays cannot turn a man into a rocky goliath or into a human torch, neither give a man invisibility or a stretching  body. Nevertheless we must acknowledge Stan Lee’s intuition that cosmic rays could interact and have actual effects on human biology.

Before detailing what cosmic rays are and where they come from, I would like to introduce some effects they provoke and introduce the scientific rationale that’s behind ALTEA investigation.

During Apollo 12 mission (1969), there was an experiment called “the Apollo helmet dosimetry experiment”, during which the signs of cosmic ray passage on an astronaut helmet were very evident.


ALTEA studies the effects of cosmic rays on central nervous system and in particular the Light Flash phenomenon. Currently light flashes are the only way that humans have to actually see elementary particles without any instrument or detector. In 1952 the physicist Cornelius Tobias predicted that cosmic rays could interact with astronaut visual system to generate anomalous perceptions of light (without the effective presence of light) . In 1969, during Apollo 11 mission, Buzz Aldrin reported the first experience of these flashes after their eyes had become adapted to the low light in the cabin. He talked about strange flashed of multiple shapes and dimensions.


After this first report, the astronauts of the following lunar missions were informed about the phenomenon and started dedicated observations. During the last lunar missions, Apollo 16 and 17, the ALFMED emulsion detector studies the correlation between the light flash perceptions and the cosmic rays.


ALFMED results showed that high energy charged particles composing cosmic rays were the effective cause of the light flashes. The interaction mechanism remained unexplained. Systematic studies on Light Flashes were carried on during the Skylab (1974) and the Apollo-Soyuz (1975) missions. In the meantime some scientist volunteered to expose themselves to low intensity particle beams to study the phenomenon in controlled conditions. Light Flashes could be reproduced by various particles passing through the eyes.

Light Flashes are highly subjective: some astronauts are particularly sensitive and can observe the phenomenon even in bright environment while others never observed any. Some astronauts are so annoyed by these flashes that cannot fell asleep. There are different shapes of flashes: stripes, multiple tracks, stars, explosions, etc..


When it’s time to link the LF phenomenon to the physics mechanisms originating them a lot of problems arise. It is needed to correlate observations from electronic detectors with astronaut sensations. The importance of these studies is given by the fact that LF could be symptoms of a wider family of more complex neuro-physiologic effects that are still hidden.

Studies on LF continued during the 90’s onboard MIR space station with the Sileye project. In the frame of this project almost 50 observation sessions were completed between 1996 and 2000 by 10 astronauts that observed more than 200 LFs. Sileye derives its name from Silicon Eye, the particle detector coupled with an helmet used for the observations. The cosmonaut wears the helmet in a dark environment and pushes a button whenever he observes a flash; in the meanwhile the particle detector measures the energy of all nuclei passing through it.

clip_image012 Cosmonaut Sergei Avdeev with Sileye-1 detector during a LF observation session onboard MIR.     clip_image014 Sileye-2 before being launched to MIR: aluminum box (on left side) contains the silicon telescope, while the yellow mask on the right is used to test dark adaptation of the astronaut.     clip_image016 
Cosmonaut Sergei Avdeev with Sileye-2 detector during a LF observation session onboard MIR.

Sileye program continued on ISS with the Alteino-Sileye3 detector, that is the link between the Sileye project and the ALTEA program. Alteino was brought onboard the International Space Station during Marco Polo Mission in 2002. First measurements were carried on by the Italian astronaut Roberto Vittori. Alteino device returned back to Earth in 2010.

Alteino-Sileye3 detector in the PIRS module of the ISS.
Light Flash observed on MIR. The increasing of LF observations at high latitudes and over the South Atlantic region is caused by different components of cosmic rays: galactic and trapped cosmic rays.

Coming soon: Radiation environment in Earth orbit.

Previous posts:
Cosmic rays and human exploration of space
ALTEA- An Italian experiment onboard the International Space Station

Further readings and sources:
Cosa sono i Light Flash (in Italian)
Light flashes (in Italian)
How can astronauts see stars with their eyes shut