Some Useful Parameters of Medical Proton Beams

Quick reference for medical proton beams from 30 to 250 MeV: beta, magnetic rigidity, range in water, and typical ionization-chamber gain.

Quick reference for medical proton beams from 30 MeV to 250 MeV: $β = v / c$ , magnetic rigidity $B ρ$ , continuous-slowing-down range in water, and a typical air-gap ionization-chamber gain per millimetre. Use it when sizing magnets, estimating penetration, or sanity-checking ionization chamber response at therapy energies.

The underlying relativity and rigidity relations are derived in Some Useful Formulae for High Energy Ion Beam Systems. Dipole and quadrupole geometry sketches are in Beam Deflection in Dipole and Quadrupole Magnets. Pyramid therapy and nozzle work sits under Particle Therapy.

Proton Beam Parameters

Energy (MeV)	$β$	$B ρ$ (T·m)	Range (cm)	IC gain (mm $^{- 1}$ )
30	0.2470	0.7977	0.884	61.2
40	0.2830	0.9236	1.486	47.7
50	0.3140	1.0353	2.224	40.3
60	0.3415	1.1370	3.089	34.5
70	0.3661	1.2313	4.075	30.8
80	0.3885	1.3197	5.176	27.8
90	0.4091	1.4033	6.389	25.2
100	0.4282	1.4830	7.707	23.5
110	0.4459	1.5593	9.128	21.9
120	0.4625	1.6327	10.65	20.5
130	0.4781	1.7036	12.26	19.4
140	0.4928	1.7723	13.96	18.5
150	0.5066	1.8391	15.76	17.5
160	0.5198	1.9041	17.63	16.8
170	0.5322	1.9675	19.59	16.2
180	0.5441	2.0295	21.63	15.4
190	0.5554	2.0902	23.74	14.8
200	0.5662	2.1496	25.93	14.4
210	0.5765	2.2080	28.19	14.2
220	0.5863	2.2654	30.52	13.6
230	0.5958	2.3218	32.91	13.5
240	0.6049	2.3774	35.37	12.9
250	0.6136	2.4321	37.90	12.5

How to read the columns

Energy: kinetic energy of the proton beam.
$β$ : lab-frame speed over $c$ . At 230 MeV, $β \approx 0.60$ : relativity is not optional for therapy protons.
$B ρ$ : magnetic rigidity; how hard a magnet must work to bend the beam. Pair with Magnetics products when choosing dipole field or bend radius ( $r = B ρ / B$ ).
Range: continuous-slowing-down approximation (CSDA) depth in water. The human body is mostly water to a fair approximation, so this is the first-order penetration figure for treatment planning checks.
IC gain: approximate ionization yield per millimetre of air gap. Useful when comparing transmission IC designs or estimating chamber current for a given fluence.

Constants

Quantity	Value	Unit
Speed of light ( $c$ )	$299792458$ (exact)	m s $^{- 1}$
Elementary charge ( $e$ )	$1.602176634 \times 1 0^{- 19}$ (exact)	C
Proton mass ( $m_{p}$ )	$1.67262192595 \times 1 0^{- 27}$	kg

Values from the 2022 CODATA recommended constants (NIST). $c$ and $e$ are exact by SI definition; $m_{p}$ is the CODATA 2022 recommended value.

Further Information

For local peak dose in pencil beams, see Local Dose in Water. Browse ionization chambers and Particle Therapy for nozzle and chamber hardware. Contact us or Support if you want a second look at an energy, rigidity, or chamber estimate for a Pyramid system.

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