Beam Energy Area-Time Cross-Scan - Electromagnetic Radiation Pressure and Momentum Step by Step

Beam energy is scanned across illuminated area and time. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Beam energy multiplies irradiance, area, and time

The finite energy window cites the irradiance source, then adds illuminated area and time as separate checked inputs.

E=IA_st=6\cdot3\cdot4=72\ \text{J}

Illuminated area scales beam energy

Hold irradiance and time fixed. Three area rows make the area-to-energy relationship explicit.

\begin{array}{c|c|c|c}I&A_s&t&E\\6\ \text{W}/\text{m}^{2}&2\ \text{m}^{2}&4\ \text{s}&48\ \text{J}\\6\ \text{W}/\text{m}^{2}&3\ \text{m}^{2}&4\ \text{s}&72\ \text{J}\\6\ \text{W}/\text{m}^{2}&4\ \text{m}^{2}&4\ \text{s}&96\ \text{J}\\\end{array}

Time window also scales beam energy

The same beam over a longer finite window carries more energy. No continuous history is assumed.

\begin{array}{c|c|c|c}I&A_s&t&E\\6\ \text{W}/\text{m}^{2}&3\ \text{m}^{2}&2\ \text{s}&36\ \text{J}\\6\ \text{W}/\text{m}^{2}&3\ \text{m}^{2}&4\ \text{s}&72\ \text{J}\\6\ \text{W}/\text{m}^{2}&3\ \text{m}^{2}&6\ \text{s}&108\ \text{J}\\\end{array}