Thermal Neutrons (Slow, < 0.5 eV)
Epithermal Neutrons (1 eV – 10 keV)
Fast Neutrons (~1 MeV)
High Energy Neutrons (~10-14 MeV)
Very High Energy (~100 MeV)
Determines the Flux-to-Dose conversion factor.
Neutron Flux:–
Dose Rate (mrem/hr):–
Dose Rate (μSv/hr):–
Total Accumulated Dose (mrem):–
Understanding Neutron Dose Rates and Radiation Safety
Calculating the neutron dose rate is a critical task in health physics, nuclear engineering, and radiation safety management. Unlike gamma radiation, neutrons interact with matter primarily through nuclear collisions rather than ionization of electron clouds. This makes measuring and shielding against neutron radiation uniquely challenging. This calculator uses the relationship between source strength, distance, and neutron energy to estimate the equivalent dose rate.
How the Calculation Works
The estimation of neutron dose involves three main physical steps:
Flux Calculation: First, we determine the neutron flux ($\phi$) at a specific distance ($r$) from the source. Assuming an isotropic point source (emitting equally in all directions) and no shielding, the flux follows the inverse square law: $\phi = S / (4\pi r^2)$, where $S$ is the source strength in neutrons per second.
Unit Conversion: The distance is converted from meters to centimeters to align with standard flux units (neutrons/cm²/s).
Flux-to-Dose Conversion: The biological damage caused by neutrons depends heavily on their energy. Fast neutrons cause more biological damage per unit of flux than thermal (slow) neutrons. We apply a conversion factor (typically derived from NCRP Report 38 or similar standards) to convert the flux ($n/cm^2/s$) into a dose rate equivalent (mrem/hr).
Neutron Energy Classifications
The biological effectiveness of neutrons varies by energy level:
Thermal Neutrons: Low energy neutrons in thermal equilibrium with their surroundings. They require a very high flux (approx. 260 $n/cm^2/s$) to generate 1 mrem/hr of dose.
Fast Neutrons: Energetic neutrons (typically resulting from fission or fusion). These are much more damaging, requiring a flux of only roughly 7 $n/cm^2/s$ to generate 1 mrem/hr.
High Energy Neutrons: Neutrons with energies above 10 MeV, often produced in accelerator facilities or specific fusion reactions.
Safety and ALARA
In radiation protection, the guiding principle is ALARA (As Low As Reasonably Achievable). To reduce the dose calculated above, safety officers employ three strategies:
Time: Reducing the time spent near the source linearly reduces the total accumulated dose.
Distance: Doubling the distance from the source reduces the dose rate by a factor of four (Inverse Square Law).
Shielding: Neutrons require hydrogen-rich materials for shielding (like water, polyethylene, or concrete) to slow them down (moderation), often followed by a material like boron or cadmium to absorb the slow neutrons.
Disclaimer: This calculator provides a theoretical estimate based on an isotropic point source in a vacuum. It does not account for backscatter (room return), attenuation by air, or shielding. For real-world safety purposes, always rely on calibrated survey meters and certified health physicists.
function calculateNeutronDose() {
// 1. Get Input Values
var sStr = document.getElementById('sourceStrength').value;
var dist = document.getElementById('distance').value;
var fluxFactor = document.getElementById('neutronEnergy').value;
var time = document.getElementById('exposureTime').value;
// 2. Validation
if (sStr === "" || dist === "" || time === "") {
alert("Please fill in all fields (Source Strength, Distance, and Time).");
return;
}
var S = parseFloat(sStr);
var r_meters = parseFloat(dist);
var factor = parseFloat(fluxFactor); // This is n/cm2/s per mrem/hr
var hours = parseFloat(time);
if (S < 0 || r_meters <= 0 || hours < 0) {
alert("Please enter valid positive numbers. Distance must be greater than 0.");
return;
}
// 3. Calculation Logic
// Convert distance to cm for Flux calculation
var r_cm = r_meters * 100;
// Calculate Surface Area of sphere (4 * pi * r^2)
var area_cm2 = 4 * Math.PI * Math.pow(r_cm, 2);
// Calculate Neutron Flux (phi) = S / Area
// Unit: neutrons / cm^2 / sec
var flux = S / area_cm2;
// Calculate Dose Rate in mrem/hr
// Formula: DoseRate = Flux / (Flux required for 1 mrem/hr)
var doseRate_mrem = flux / factor;
// Convert mrem/hr to microSieverts/hr (uSv/hr)
// 1 mrem = 10 uSv
var doseRate_uSv = doseRate_mrem * 10;
// Calculate Total Dose
var totalDose = doseRate_mrem * hours;
// 4. Update UI
document.getElementById('resFlux').innerText = formatNumber(flux) + " n/cm²/s";
document.getElementById('resMrem').innerText = formatNumber(doseRate_mrem);
document.getElementById('resUsSv').innerText = formatNumber(doseRate_uSv);
document.getElementById('resTotal').innerText = formatNumber(totalDose);
// Show results
document.getElementById('results').style.display = "block";
}
function formatNumber(num) {
if (num === 0) return "0";
// If number is very small or very large, use scientific notation
if (num 10000) {
return num.toExponential(3);
}
return num.toFixed(3);
}