User talk:Geek3/Archives/2016

a single subject

Dear Geek3,

I’m Solo. I posted you sometime ago (october-november 2013; june 2015) about very basic questions on magnetic fields that I had in mind, though some of them were very simple and you helped me to understand it. however, this time I’d like to share with you a very different subject that preceded the former ones, though for some reason I had preferred not to tell you. if you would allow me, I would like to get down to brass tacks in an as short as possible manner for me. please, excuse me for using plain words, since my technical knowledges are much more limited than yours.

according to Earnshaw’s theorem (I understand its basic concept only) it is not possible to generate a static magnetic field to confine charged particles because of (if I’m not wrong) the divergence factor in the inner B field lines, and this is aplied to magnetic and electrostatic fields. However, the Quadrupole Ion Trap demonstrates that if we apply an AC to its poles (it seems there may be other possible configurations) with a certain radio frequency, this principle may be relatively overcomed due to the alternating combination of two opposite static states of confinement and anti-confinement, trapping in this way the ions in a central area.

if we extrapolate this same phenomenon from electrostatic fields to magnetic fields, some interesting questions may arise in our mind. if we take from your Gallery, for instance, your “magnetic quadrupole field” we can see something similar to the Ion Trap, though it could never work with DC only. moreover, it doesn’t cover the basic three directions of space, a necessary minimal condition for the confinement of charged particles, and that’s probably because of the limitations of its geometry. if we take your “fields of four, six, eight and ten wires” we can see approximately the same. even if they were ring coils instead of wires, since their cross section view would be the same, the B field lines external to the magnetic rings would behave in a very different manner due to the geometrical limitations of these patterns too, and this is why simply appling an AC to these configurations would be not enough to make them work for ionic confination.

now I’d like to show you something: https://sites.google.com/site/asingleapproach/ to avoid wasting your time, you can take a look directly at the three images in section “3 the single-pointed concept”. these are three different configurations for inertial magnetic confinement using a same constructive principle I found some years ago, and the only object of this last post is asking you what do you see there when appling a high frequency AC to these magnets, since I’m not sure if what I see is technically feasible because I might be ignoring some aspects yet. additional explanations are included in the full text (12 pages more or less), but perhaps you don’t need to read them all. the main conclusions are summarized at sections “8 objections to this approach” and “9 some interesting replies”. the other sections are more speculative. I’m still enjoying of your images. they are the best background I’ve found to understand some basic magnetic interactions.

Dear Solo,

A few remarks to the coil configuration you posted: First of all (if I understood correctly) the coils will produce zero magnetic field in the center due to symmetry reasons, as is the case for the quadrupole field that I plotted. But this does not at all mean that there is a potential or energy minimum which could trap particles, it means there is no magnetic field, i.e. particles in the center will feel no magnetic force (particles with a dipole moment can be trapped where abs(B) is lowest as so-called low field seekers, but the trapping forces are tiny). Second, your coils will have currents running in opposite directions close to each other, which will nearly cancel each others fields, and therefore will make the total produced field small, i.e. much less than a Tesla. Third, you can not have a rapid oscillating AC magnetic field, because any coil has an inductance that makes it harder to change the current the faster you try.

If you think about nuclear fusion, particles need to be fast, i.e. hot, which means they will move at large radii (meters) in a given magnetic field. The movement in a circle is already closed, which is great, but then the particles are still free to move along magnetic field lines. That is why the current concepts of a fusion reactor (tokamak, stellerator) try to close the magnetic fields along a torus. Unfortunately the bending of the torus creates problems and this where today's fusion research starts...

If you want to gain a deeper understanding of the subject, I highly recommend to stand on the shoulders of giants and read some of the classic introductory textbooks on topics like particle trapping and plasma physics. Best regards, --Geek3 (talk) 23:03, 4 February 2016 (UTC)

VectorFieldPlot

Hi. I try to make image of vector field ${\dot {z}}=z^{3}$ , like in http://arxiv.org/pdf/1506.07120v1.pdf image 1.b. How can I do it with VectorFieldPlot ? ( I can run script and create example image and I know that re(z^3) = x^3-3*x*y^2 and im(z^3) = 3*y*x^2-y^3. TIA --Adam majewski (talk) 22:03, 16 February 2016 (UTC)

You can define a new field element just where all the other elements (monopoles, wires, etc.) are defined:

for r3 in self.get_elements('r3'):
    r = xy - sc.array(r3[:2])
    x, y = tuple(r)
    Fxy += sc.array([x**3 - 3*x*y**2, 3*y*x**2 - y**3])

Then you create a field containing that element:

doc = FieldplotDocument('VFPt_r3', commons=True, width=600, height=600)
field = Field({'r3':[[0,0]]})
n = 5
for s in ((a, b) for a in (-1,1) for b in (-1,1)):
    for i in range(n):
        line = FieldLine(field, [s[0]*i*3./n, s[1]*i*3./n], directions='both')
        doc.draw_line(line, arrows_style={'dist':1.5})
doc.write()

This should do the trick. --Geek3 (talk) 10:08, 21 February 2016 (UTC)

thx for the answer.

 # r3
        for r3 in self.get_elements('r3'):
            r = xy - sc.array(r3[:2])
            x, y = tuple(r)
            Fxy += sc.array([x**3 - 3*x*y**2, 3*y*x**2 - y**3])
     
    
    def Fn(self, xy):
        '''
        returns the normalized field force, i.e. direction of field lines
        '''
        force = self.F(xy)
        d = vabs(force)
        if (d != 0.): return force / d
        return sc.array([0., 0.])

### append your specific field creation here ###
# see http://commons.wikimedia.org/wiki/File:VFPt_charges_plus_minus.svg for an exampledoc = FieldplotDocument('VFPt_charges_plus_minus', commons=True)



doc = FieldplotDocument('VFPt_r3', commons=True, width=600, height=600)
field = Field({'r3':[[0,0]]})
n = 5
for s in ((a, b) for a in (-1,1) for b in (-1,1)):
    for i in range(n):
        line = FieldLine(field, [s[0]*i*3./n, s[1]*i*3./n], directions='both')
        doc.draw_line(line, arrows_style={'dist':1.5})
doc.write()

It works byt the svg file is empty = good svg file wthout any drawings. ??? --Adam majewski (talk) 14:27, 21 February 2016 (UTC)

I think the problem is that you placed for r3 in self.get_elements('r3'): after the return Fxy statement. Therefore an empty field is returned. Can you check? --Geek3 (talk) 14:49, 21 February 2016 (UTC)

Now it works. Thx.

The plane is (-1,1)x (-1,1) ? Is it possible to add field lines along axes ? The shape of field lines in the reference image seems different to me , do you have similar feeling ? --Adam majewski (talk) 20:10, 21 February 2016 (UTC)

The standard unit is 100, which makes the plane go from -3 to +3, but the unit can be changed when the FieldplotDocument is created. Sure you can add field lines along the axes if you change the starting points of the lines. They are now placed on a diagonal cross. The field lines in the reference image look a little different indeed. That is because they are not accurately plotted, but just sketched as Beziers. Note that the outer circle is not part of the field. --Geek3 (talk)

Quality Image Promotion

Your image has been reviewed and promoted Congratulations! VFPt charges plus minus thumb.svg, which was produced by you, was reviewed and has now been promoted to Quality Image status. If you would like to nominate another image, please do so at Quality images candidates. We also invite you to take part in the categorization of recently promoted quality images. Comments Good quality. --Cccefalon 11:42, 8 June 2016 (UTC)

--QICbot (talk) 05:28, 11 June 2016 (UTC)

Quality Image Promotion

Your image has been reviewed and promoted Congratulations! Mplwp resonance zeta envelope.svg, which was produced by you, was reviewed and has now been promoted to Quality Image status. If you would like to nominate another image, please do so at Quality images candidates. We also invite you to take part in the categorization of recently promoted quality images. Comments Please see my annotations for the necessary improvements. --Cccefalon 11:45, 8 June 2016 (UTC) Done I have changed the labels to the same number of digits. Marking of the zero-point is deliberately like this to have both axes marked clearly. --Geek3 9:54, 9 June 2016 (UTC) ok then --Cccefalon 04:56, 10 June 2016 (UTC)

--QICbot (talk) 05:23, 12 June 2016 (UTC)

Quality Image Promotion

Your image has been reviewed and promoted Congratulations! VFPt cylindrical magnet thumb.svg, which was produced by you, was reviewed and has now been promoted to Quality Image status. If you would like to nominate another image, please do so at Quality images candidates. We also invite you to take part in the categorization of recently promoted quality images. Comments Good quality. --Cccefalon 13:09, 10 June 2016 (UTC)

--QICbot (talk) 05:25, 13 June 2016 (UTC)

Quality Image Promotion

Your image has been reviewed and promoted Congratulations! Mplwp ballistic trajectories angles.svg, which was produced by you, was reviewed and has now been promoted to Quality Image status. If you would like to nominate another image, please do so at Quality images candidates. We also invite you to take part in the categorization of recently promoted quality images. Comments Please have the legend full-opaque. See my note. --Cccefalon 21:49, 11 June 2016 (UTC) Done --Geek3 13:07, 12 June 2016 (UTC) Much better! Please observe my hint about keeping the legends outlfine in distance to the dashed lines. --Cccefalon 21:35, 12 June 2016 (UTC)

Your image has been reviewed and promoted Congratulations! Mplwp factorial gamma stirling.svg, which was produced by you, was reviewed and has now been promoted to Quality Image status. If you would like to nominate another image, please do so at Quality images candidates. We also invite you to take part in the categorization of recently promoted quality images. Comments Same as before. The dashed lines in the legend affect the readability in a print. --Cccefalon 21:50, 11 June 2016 (UTC) Done --Geek3 13:07, 12 June 2016 (UTC) Much better! Please observe my hint about keeping the legends outlfine in distance to the dashed lines. --Cccefalon 21:35, 12 June 2016 (UTC)

--QICbot (talk) 05:26, 15 June 2016 (UTC)

Wireframe Sphere Math

Geek3, Thank you for your wireframe sphere. I am translating it to Python. I will use it to draw celestial navigation diagrams. Please point me to a reference for the math you used. — Preceding unsigned comment added by Gewoods3 (talk • contribs) 01:29, 29 October 2016 (UTC)

Hi Gewoods3, all the math I used is standard high-school vector geometry, and can be found all over wikipedia. So basically you have to imagine 3D-space and parametrize the meridians and circles of latitude in polar coordinates. This will give you a parametric vector function with trigonometric expressions, for example XYZ=(cos(lon)*cos(lat), sin(lon)cos(lat), sin(lat)). You can rotate anything in space by applying a rotation transform (en:Rotation_formalisms_in_three_dimensions). Finally you apply a projection from 3D into 2D space, for instance by simply cutting away one of the cartesian coordinates. This will give you the desired coordinates in the image plane. Unfortunately, the code that I have used is also not easier to understand... --Geek3 (talk) 15:00, 29 October 2016 (UTC)