Design Guide › Physics theory
Physics theory design rules
4 of the guide’s 1374 rules carry the physics-theory tag.
Rules that are theoretical results rather than practice: stripping lifetimes, measurement accuracy floors, kinematic broadening, and detector efficiency models.
Each rule keeps its formula where the source gives one, a verbatim quote, a page-level
citation, and a stable identifier (dg-NNNN) that resolves here and on the
all-in-one guide.
To combine this tag with another (rules carrying both), use the filterable view: /design-guide/?domain=physics-theory and add a second chip. Related domains, by how often they share a rule with this one: Beam measurement (2), Detectors (1), Extraction (1), Magnet (1).
Verify before use. Every rule here is a source extract in the vocabulary of the editorial methodology — faithful to its cited page, not an independently validated engineering requirement. Re-read any rule that drives a real design decision at the cited page before committing metal, money, or high voltage to it.
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Lorentz (magnetic) stripping of H- has rest-frame lifetime tau = (A1/E)*exp(A2/E) with A1=2.714e-6 s*V/m, A2=4.474e9 V/m, E=gamma*beta*c*B - negligible below a few MeV even at 4 T.
tau = (A1/E)*exp(A2/E), E = gamma*beta*c*BSource, quote & tabletop applicability
a 4 T magnetic field for the maximum achievable energy of 8.5 MeV in the AMIT cyclotron corresponds to a beam-rest-frame electric field of E = 160 MV/m. This entails a marginal beam fraction loss per unit length of 1.42e-6 m-1
Calvo et al., Beam Stripping Interactions in Compact Cyclotrons — PRAB 24, 090101 (2021) — p. 7-8, 14
Tabletop: At 0.889 T and 500 keV the rest-frame field is ~9 MV/m, where the exponential makes the lifetime effectively infinite - Lorentz stripping can be ignored entirely for a next machine.
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Know the accuracy floor of any absorber-based energy measurement: range-energy data and straggling limit the most-probable-energy determination to a few hundred keV, the high-energy edge of the distribution is nearly as good, but the LOW-energy side of the spectrum is largely unrecoverable.
Source, quote & tabletop applicability
These factors limit the accuracy of determination of the most probable energy to a few hundred kilovolts. The high energy portion of the energy distribution can be determined with almost equivalent accuracy
Tabletop: Scale the absolute numbers down with energy, but keep the shape of the claim — quote the high-energy edge with confidence, treat the low-energy tail as semi-quantitative. Same asymmetry applies to a PIPS-plus-degrader spectrum on a next machine, and to interpreting any resonance-yield curve taken with a spread beam.
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Mounting a spectrograph with its dispersion plane horizontal costs kinematic broadening of peaks (from the in-plane angular acceptance) when scattering off light nuclei, but can buy large-angle reach - here rotation to 165 degrees, needed for back-angle cross sections and DWBA tests. Know which trade you are making.
Source, quote & tabletop applicability
In scattering from light nuclei, this introduces appreciable kinematic broadening of peaks as the entrance aperture is opened.
Tabletop: SCALE-HONEST - kinematic broadening scales with (m_projectile/m_target) and aperture, not beam energy, so the trade is identical for a next machine's Rutherford-scattering station. The fix they note (close the entrance aperture when it matters) is the standard resolution-vs-count-rate knob students should learn to turn.
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A simple single-scattering model predicts organic-scintillator neutron efficiency to satisfactory accuracy: eff = (1 - E0/En) * (1 - exp(-nH*sigma_np*l)), where the first factor (fraction of recoils above threshold) is exact and independent of the scintillator response shape so long as response is monotonic; find E0 per threshold setting from a D(d,n) check and take sigma_np from Gammel's semi-empirical formula (good to parts in 10^3 up to 42 MeV).
eff = (1 - E0/En)(1 - exp(-n_H * sigma_np(En) * l)); assumptions - n-p single scattering only, effective length = geometric length, recoil range negligibleSource, quote & tabletop applicability
The first factor in (1) is exact. It does not depend on the exact shape of the response curve (pulse-height vs proton recoil energy) of the scintillator.
Fulbright et al., A Fast Neutron Time of Flight System for Use with Cyclotrons — NYO-9360 (1962) — p. 15
Tabletop: DIRECT for any neutron-counting next-machine experiment and a lovely teaching derivation - a two-factor closed form students can test against a calibration reaction. The identification of which factor is exact vs model-dependent is the transferable habit.