# User query: Can I have an applied field changing both in time and in space?¶

You can simulate an applied field which both changes in space and time: this may be useful to mimic the effect of a write head on the magnetic grains of an hard disk while the head is moving.
The way we do this is by changing the applied field every delta_t picoseconds. This means that the applied field won't change continuously in time: it will be piecewise constant in time (but, in general, it can be non uniform in space).
You can do something like that:

`````` 1 import math
2
3 def set_H(sim):
4   width = 10.0        # nm
5   v = 100.0           # nm/ns == m/s
6   H_amplitude = 0.5e6 # A/m
7
8   t = float(sim.time/SI(1e-9, 's')) # get the time in ns
9   center = (v*t, 0, 0) # center of the applied field region
10   def H(r):
11     x, y, z = [ri/1e-9 - ci for ri, ci in zip(r, center)]
12     factor = H_amplitude*math.exp(-(x*x + y*y + z*z)/(width*width))
13     return [factor, factor, factor]
14
15   sim.set_H_ext(H, unit=SI('A/m'))
16
17 sim.relax(do=[(set_H, every('time', SI(50e-12, 's'))),
18               ('exit', at('time', SI(1000e-12, 's')))])
``````

The function set_H is called every 50 ps and does the following: it sets a new field from the function H(r).
This function sets a field which directed along the direction [1, 1, 1] and almost vanishes outside a sphere with radius ~ 30.0 nm.
The center of this sphere moves along the direction [1, 0, 0] with velocity 100 nm/ns, thus simulating the motion of a write head in a hard disk.
Obviously the piece of code is not complete, it shows only the technique in order to have a field changing in time and space.
For a complete example see the next section.

## Complete example: simple moving write-head example¶

Here is a simulation of five cubes made of cobalt and a write-head which moves on the top of the cubes and applies a time-varying field in order to change their magnetisation. At the beginning the magnetisation of all the cubes is pointing in the [0, 0, 1] direction. After the write-head has passed over the cubes, the magnetisation of cube 1, 3 and 5 are switched in the opposite direction, while cube 2 and 4 have unchanged magnetisation.
This is possible because the write-head field, which is space-dependent (being intense only inside a sphere of radius 15-20 nm), changes also in time. It indeed translates in space, but also change in intensity, being directed in the [0, 0, -1] direction when the sphere is at the center of cube 1, 3 and 5 and in the [0, 0, 1] direction when the center of the sphere is in cube 2 and 4.

Here is the geo file used to generate the mesh (Netgen):

```algebraic3d

# cubes
solid cube1 = orthobrick (    0, 0, 0;  20.0, 20.0, 20.0) -maxh = 2;
solid cube2 = orthobrick ( 30.0, 0, 0;  50.0, 20.0, 20.0) -maxh = 2;
solid cube3 = orthobrick ( 60.0, 0, 0;  80.0, 20.0, 20.0) -maxh = 2;
solid cube4 = orthobrick ( 90.0, 0, 0; 110.0, 20.0, 20.0) -maxh = 2;
solid cube5 = orthobrick (120.0, 0, 0; 140.0, 20.0, 20.0) -maxh = 2;

tlo cube1;
tlo cube2;
tlo cube3;
tlo cube4;
tlo cube5;
```

And here is the full listing of the example:

`````` 1 from nmag.common import *
2 import math
3
4 # Define magnetic material (data from OOMMF materials file)
5 mat_Co = MagMaterial(name="Co",
6                      Ms=SI(1400e3, "A/m"),
7                      exchange_coupling=SI(30e-12, "J/m"),
8                      anisotropy=uniaxial_anisotropy(axis=[0, 0, 1],
9                                                     K1=SI(520e3, "J/m^3")))
10 sim = Simulation()
12               [('cube1', mat_Co), ('cube2', mat_Co), ('cube3', mat_Co),
13                ('cube4', mat_Co), ('cube5', mat_Co)],
14               unit_length=SI(1e-9, 'm'))
15
16 sim.set_m([0, 0, 1])
17
18 sim.relax(save=[('fields', at('convergence'))])
19
20 t0 = [sim.time]
21
22 def set_H(sim):
23     t = float((sim.time - t0)/SI(1e-9, 's'))  # get time in ns
24     width = 10.0                                 # nm
25     v = 25.0                                     # nm/ns = m/s
26     H_amplitude = 4.0e6*math.sin(math.pi*t)      # A/m
27     center = (v*t, 20, 10)
28     print "CENTER IN", center
29     def H(r):
30         x, y, z = [ri/1e-9 - ci for ri, ci in zip(r, center)]
31         factor = H_amplitude*math.exp(-(x*x + y*y + z*z)/(width*width))
32         return [0, 0, -factor]
33
34     sim.set_H_ext(H, unit=SI('A/m'))
35
36 set_H(sim)
37
38 sim.set_params(stopping_dm_dt=0*degrees_per_ns)
39
40 sim.relax(save=[('fields', every('time', SI(200e-12, 's'), first=t0))],
41           do=[(set_H, every('time', SI(50e-12, 's'), first=t0)),
42               ('exit', at('time', SI(6000e-12, 's')))])
``````

Here is the magnetisation at the beginning of the simulation, after the first relax command (whose purpose is just to find the zero field magnetisation configuration): and here is the magnetisation after the write-head has passed over the cubes: Also available in: HTML TXT