space charge: copy from SpaceChargeBunched to new interpolated profil…

…e class

pysixtrack/be_beamfields/spacecharge.py

@@ -143,3 +143,78 @@ def track(self, p):
             p.py = py
 
 
+class SpaceChargeInterpolatedProfile(Element):
+    """Space charge for a bunched beam with discretised profile."""
+
+    _description = [
+        ("number_of_particles", "", "Number of particles in the bunch", 0.0),
+        ("line_density_profile", "1/m", "Discretised list of density values with integral normalised to 1", [1.0]),
+        ("dz", "m", "Unit distance between profile points", 0.0),
+        ("z0", "m", "Start position of line density profile", 0.0),
+        ("sigma_x", "m", "Horizontal size of the beam (r.m.s.)", 1.0),
+        ("sigma_y", "m", "Vertical size of the beam (r.m.s.)", 1.0),
+        ("length", "m", "Integration length of space charge kick", 0.0),
+        ("x_co", "m", "Horizontal closed orbit offset", 0.0),
+        ("y_co", "m", "Vertical closed orbit offset", 0.0),
+    ]
+    _extra = [
+        ("min_sigma_diff", "m", "Threshold to detect round beam", 1e-30),
+        ("enabled", "", "Switch to disable space charge effect", True),
+    ]
+
+    def track(self, p):
+        if self.enabled:
+            pi = p._m.pi
+            exp = p._m.exp
+            sqrt = p._m.sqrt
+            bunchlength_rms = self.bunchlength_rms
+            length = self.length
+            sigma_x = self.sigma_x
+            sigma_y = self.sigma_y
+
+            charge = p.q0 * p.echarge
+            x = p.x - self.x_co
+            px = p.px
+            y = p.y - self.y_co
+            py = p.py
+            sigma = p.sigma
+
+            chi = p.chi
+
+            beta = p.beta0 / p.rvv
+            p0c = p.p0c * p.echarge
+
+            Ex, Ey = get_Ex_Ey_Gx_Gy_gauss(
+                x,
+                y,
+                sigma_x,
+                sigma_y,
+                min_sigma_diff=1e-10,
+                skip_Gs=True,
+                mathlib=p._m,
+            )
+
+            fact_kick = (
+                chi
+                * (charge * p.qratio)
+                * charge
+                * (1 - p.beta0 * beta)
+                / (p0c * beta)
+                * length
+            )
+
+            fact_kick *= (
+                self.number_of_particles
+                / (bunchlength_rms * sqrt(2 * pi))
+                * exp(
+                    -0.5
+                    * (sigma / bunchlength_rms)
+                    * (sigma / bunchlength_rms)
+                )
+            )
+
+            px += fact_kick * Ex
+            py += fact_kick * Ey
+
+            p.px = px
+            p.py = py