Add Root helper struct

src/muons.jl

@@ -562,3 +562,53 @@ end
 
 #   return value;
 # }
+
+"""
+    Root(R, n, t)
+
+Helper struct to find solution(s) to ``z`` of the square root expression:
+
+```math
+\begin{aligned}
+ct(z=0) & = & z + n \sqrt{z^2 + R^2}
+\end{aligned}
+```
+
+where ``n = 1/\cos(\theta_{c})`` is the index of refraction.
+
+# Arguments
+
+- `R`: minimal distance of approach [m]
+- `n`: index of refraction
+- `t`: time at z = 0 [ns]
+
+# Fields
+
+- `most_upstream`: most upstream solution
+- `most_downstream`: most downstream solution
+- `isvalid`: validity of the solution
+```
+"""
+struct Root
+    most_upstream::Float64
+    most_downstream::Float64
+    isvalid::Bool
+
+    function Root(R, n, t)
+        a = n^2 - 1.0
+        b = 2 * C * t
+        c = R^2 * n^2 - C^2 * t^2
+
+        q = b * b - 4 * a * c
+
+        isvalid = false
+        if q >= 0.0
+
+            first = (-b - sqrt(q)) / (2a)
+            second = (-b + sqrt(q)) / (2a)
+
+            isvalid = C * t > second
+        end
+        new(first, second, isvalid)
+    end
+end