## The Galileo Energetic Particles Detector

## Galileo EPD Handbook

### Chapter 1. Instrument Summary

**Charged Particle Response of Magnetic Deflection System
for Galileo Jupiter Orbiter**** ****(draft)***
(continued)*

**Methods of Calculation**

We divided a detector surface into smaller sample areas,
each measuring 0.08 x 0.08 cm^{2}. The center of the sample
area is used as an initial position called a sample point.
Starting from a sample point on a detector, we chose
uniformly distributed polar and azimuthal angles and
approximately logarithmically spaced energies for the
particles. The equations of motion (equations (1) and (2))
are solved numerically using a fourth-order
predictor-corrector method in a time-reversed sense. Along a
solved trajectory, every line segment is composed of two
points (x_{i}, y_{i}, z_{i} and x_{i+1}, y_{i+1}, z_{i+1}). Each
line segment was tested against all detector surfaces, the
side surfaces, the aperture surfaces, and the channel
surfaces in order to determine whether the trajectory passes
the sensor or not. Each test is performed by examining if
the intersection point of a line segment is inside or
outside the boundaries of the surfaces as described in Figure 6.

By using this method, we can determine if a particle collides with the interior surfaces or goes through any of the detectors. This process can be repeated for the purpose of scanning different polar and azimuthal angles to form a set of trajectories of the particle. Then, for this starting point, the number of detected particles can be determined and the solid angle spanned by the set of trajectories can be computed. After examining all sample areas, the geometric factor for this energy and the detector can be obtained by using equation (11).

Figure 7 shows that an electron trajectory intersects with a detector segment in the coordinate system of the simulation. The polar and azimuthal angles are also shown for the calculation of the geometric factors. The geometric factor of detectors at a given energy is defined as follows:

where ΔA is the sample area and n is the number of sample areas. ΔΩ is the solid angle spanned by open trajectories. It also depends upon the energy of the particle and the number of detected particles (or the number of open trajectories).

Figure 7.
A segment of electron trajectory intersects with a
detector. ΔA is the sample area on the
detector and θand φ are
the polar and azimuthal angles, respectively. |

For a particular energy of the particle at a starting point, the solid angle can be evaluated:

where Δθ and Δφ are the scanning angle intervals. Since we used 1° and in some cases 0.5° for Δθ or Δφ, the approximation is justified.

Next: Results of the Simulation

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Updated 8/23/19, Cameron Crane

## QUICK FACTS

**Manufacturer:**The Galileo Spacecraft was manufactured by the Jet Propulsion Laboratory, Messerschmitt-Bölkow-Blohm, General Electric, and the Hughes Aircraft Company.

**Mission Duration:**Galileo was planned to have a mission duration of around 8 years, but was kept in operation for 13 years, 11 months, and 3 days, until it was destroyed in a controlled impact with Jupiter on September 21, 2003.

**Destination:**Galileo's destination was Jupiter and its moons, which it orbitted for 7 years, 9 months, and 13 days.