Geometric scaling of laser-driven proton focusing from hemispherical foils

We systematically characterize the focusing behavior of laser-driven proton beams from hemispherical targets of various diameters using mesh radiography. The proton focal location is inferred to be near the geometrical center for the smallest tested hemisphere ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mi mathvariant="normal">Ψ</a:mi> <a:mo>=</a:mo> <a:msub> <a:mi>D</a:mi> <a:mtext>hemi</a:mtext> </a:msub> <a:mo>/</a:mo> <a:msub> <a:mi>D</a:mi> <a:mtext>Laser</a:mtext> </a:msub> <a:mo>=</a:mo> <a:mn>6.1</a:mn> </a:mrow> </a:math> ). However, larger hemispheres ( <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:mi mathvariant="normal">Ψ</c:mi> <c:mo>=</c:mo> <c:mn>14.6</c:mn> </c:mrow> </c:math> ) degrade the focusing behavior and behave more like flat foils with focal location significantly inside the hemisphere. We also infer a tight virtual focus of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mrow> <e:mn>9</e:mn> <e:mo>±</e:mo> <e:mn>3</e:mn> <e:mspace width="0.28em"/> <e:mi>μ</e:mi> <e:mi mathvariant="normal">m</e:mi> </e:mrow> </e:math> through a mesh transition analysis.