Please enter all required values.
RESULTS
Input Parameters Specification
Cathode RadiusInner cathode radius in meters used for Hull cutoff potential.
Anode RadiusOuter anode radius in meters for the magnetron interaction region.
Magnetic FieldApplied magnetic flux density in Wb/m².
Frequency & ResonatorsGHz tuning frequency and resonator count for Hartree potential.
Practical Operational Examples
Hull Cutoff
Estimate the cutoff voltage using cathode radius, anode radius and magnetic field.
Hartree Potential
Estimate microwave magnetron Hartree potential using frequency and resonator count.
Microwave Tube Study
Use the result when comparing anode-cathode geometry, magnetic field strength and operating voltage.
Resonator Effect
Change the number of resonators to see how Hartree potential shifts in the preserved formula.
Diagrams & Theory
Resonant cavity magnetron structure with output coupling loop, resonating cavities, copper anode block, oxide-coated cathode and heater leads.
Formulas & Mathematical Logic
Step 1: Read cathode radius a, anode radius b, magnetic field B, frequency Fr and resonator count N.
Step 2: Electron mass m = 9.11 × 10^-31 kg and electron charge e = 1.6 × 10^-19 C.
Step 3: m1 = 1 - (a² / b²).
Step 4: Hull cutoff potential = ((e × b² × B²) / (8 × m)) × m1² / 1000.
Step 5: Hartree potential = ((2 × π × Fr × 10^9 × B) / N) × (b² - a²) / 1000.
Step-by-Step Example
Example: cathode radius = 0.005 m, anode radius = 0.04 m, magnetic field = 0.1 Wb/m², frequency = 2.45 GHz, resonators = 8.
Step 1: Calculate radius ratio term: m1 = 1 - (a² / b²).
Step 2: Use magnetic field and anode radius in the Hull cutoff expression.
Step 3: Divide Hull cutoff result by 1000 to display kV.
Step 4: Use frequency, magnetic field, resonator count and radius difference in the Hartree expression.
Step 5: Divide Hartree result by 1000 to display kV.
How to Use This Calculator
Enter cathode radius in meters.
Enter anode radius in meters.
Enter magnetic field in Wb/m².
Enter tuning frequency in GHz.
Enter the number of resonators.
Click Calculate to get Hull cutoff potential and Hartree potential in kV.
About This Calculator
Estimate magnetron Hull cutoff and Hartree potential from geometry and magnetic field.
The CalcBoy Magnetron Calculator calculates Hull cutoff potential and Hartree potential using cathode radius, anode radius, magnetic field, frequency and resonator count.
A cavity magnetron is a high-power microwave oscillator where electrons move in crossed electric and magnetic fields. The cathode emits electrons, the anode block contains resonant cavities, and the magnetic field controls the curved electron paths. Two important theoretical voltage estimates are Hull cutoff potential and Hartree potential.
Hull cutoff potential relates to the voltage condition where electrons just reach the anode under the applied magnetic field and magnetron geometry. Hartree potential gives another operating-related voltage estimate that includes tuning frequency and the number of resonators. These calculations are useful for study, microwave tube theory, educational design checks and comparing how radius, field strength and frequency affect magnetron behavior.
This calculator is intended for engineering learning and theoretical estimation. Real magnetron operation also depends on cathode emission, cavity shape, mode structure, thermal design, magnetic circuit, vacuum condition, output coupling, insulation and high-voltage safety.
Best UseMagnetron theory and microwave tube voltage estimates.
Supported InputsCathode radius, anode radius, magnetic field, frequency and resonator count.
Helpful ForHull cutoff, Hartree potential, microwave oscillator study and cavity magnetron analysis.
Design ReminderMagnetrons use dangerous high voltage and microwave energy.
Safety note: Magnetron circuits can contain lethal high voltage even after power is removed. This calculator is for theory and study, not hands-on microwave oven repair guidance.
Frequently Asked Questions
What is Hull cutoff potential?
Hull cutoff potential is a theoretical magnetron voltage condition related to electron motion between cathode and anode under magnetic field.
What is Hartree potential?
Hartree potential is a magnetron voltage estimate that includes magnetic field, operating frequency, resonator count and anode-cathode geometry.
What unit is magnetic field entered in?
Magnetic field is entered in Wb/m², which is equivalent to tesla.
Why are cathode and anode radius important?
The radius difference defines the electron interaction region and strongly affects the calculated potentials.
Can this be used for microwave oven repair?
No. It is a theory calculator. Microwave oven magnetrons involve lethal high voltage and should not be serviced casually.
What unit are results shown in?
Both Hull cutoff potential and Hartree potential are displayed in kilovolts.
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